LIFE LEXICON Release 17, 2000 August 24 ASCII version INTRODUCTION This is a lexicon of terms relating to John Horton Conway's Game of Life. It is also available in an HTML version. This lexicon was compiled by Stephen A. Silver - see below for additional credits. I can be contacted at life@argentum.freeserve.co.uk. The lastest version of this lexicon should always be available from the Life Lexicon Home Page at http://www.argentum.freeserve.co.uk/lex_home.htm. CREDITS The largest single source for the early versions of this lexicon was a glossary compiled by Alan Hensel "with indispensable help from John Conway, Dean Hickerson, David Bell, Bill Gosper, Bob Wainwright, Noam Elkies, Nathan Thompson, Harold McIntosh, and Dan Hoey". Other sources include the works listed in the bibliography at the end of this lexicon, as well as pattern collections by Alan Hensel and David Bell (and especially Dean Hickerson's file stamp.l in the latter collection), and the web sites of Mark Niemiec, Paul Callahan, Achim Flammenkamp, Robert Wainwright and Heinrich Koenig. Recent releases also use a lot of information from Dean Hickerson's header to his 1995 stamp file (http://math.ucdavis.edu/~dean/RLE/stamps.html). Most of the information on recent results is from the discoverers themselves. David Bell, Nick Gotts, Alan Hensel, Dean Hickerson, Dieter Leithner, Peter Rott and Malcolm Tyrrell all provided useful comments on earlier releases of this lexicon. The format, errors, use of British English and anything else you might want to complain about are by Stephen Silver. COPYING This lexicon is copyright (C) Stephen Silver, 1997-2000. It may be freely copied and/or modified as long as due credit is given. This includes not just credit to those who have contributed in some way to the present version (see above), but also credit to those who have made any modifications. LEXICOGRAPHIC ORDER I have adopted the following convention: all characters (including spaces) other than letters and digits are ignored for the purposes of ordering the entries in this lexicon. (Many terms are used by some people as a single word, with or without a hyphen, and by others as two words. My convention means that I do not have to list these in two separate places. Indeed, I list them only once, choosing whichever form seems most common or sensible.) Digits lexicographically precede letters. FORMAT The format used in the ASCII version of this lexicon is loosely based on that of the Jargon File. In particular, the keywords are enclosed in colons and selected references to them are enclosed in curly brackets. The curly brackets will not be of much use unless you have a programmable text editor, in which case you could program it to jump from a reference to the corresponding definition when you hit a certain key. (The file lifelex.el, which you should have received with this lexicon, provides such a facility for GNU Emacs.) If you don't want the curly brackets you can safely remove them with two find and replace operations, since they are not used for any other purpose in this file. The colons are more generally useful. For example, a search for ":foo" will take you straight to the definition of the first word beginning with "foo" (or at least it would if there were any). This is the recommended way of finding a particular definition. The diagrams in this lexicon are in a very standard format. You should be able to simply copy a pattern, paste it into a new file and run it in your favourite Life program. If you use Johan Bontes' Life32 or Mirek Wojtowicz' MCell then you can, of course, paste the pattern directly into the Life program. If you view this lexicon in GNU Emacs and use lifelex.el then you should be able to load a pattern into your Life program with a single keypress, without needing to copy or paste. The diagrams use an asterisk to represent a live cell. If this looks ugly with the font you use then you can change to O or o with a global replace. I have restricted myself to diagrams of size 64x64 or less. Most definitions that have a diagram have also some data in brackets after the keyword. Oscillators are maked as pn (where n is a positive integer), meaning that the period is n (p1 indicates a still life). Wicks are marked in the same way but with the word "wick" added. For spaceships the speed (as a fraction of c, the speed of light), the direction and the period are given. Fuses are marked with speed and period and have the word "fuse" added. Wicks and fuses are infinite in extent and so have necessarily been truncated, with the ends stabilized wherever practical. SCOPE This lexicon covers only Conway's Life, and provides no information about other cellular automata. David Bell has written articles on two other interesting cellular automata: HighLife (which is similar to Life, but has a tiny replicator) and Day & Night (which is very different, but exhibits many of the same phenomena). These articles can be found on his web-site (http://canb.auug.org.au/~dbell/). ERRORS AND OMISSIONS If you find any errors or serious omissions, then please let me know. NAMES When deciding whether to use full or abbreviated forms of forenames I have tried, wherever possible, to follow the usage of the person concerned. QUOTE Every other author may aspire to praise; the lexicographer can only hope to escape reproach. -- Samuel Johnson, 1775 DEDICATION This lexicon is dedicated to the memory of Dieter Leithner, who died on 26 February 1999. ----------------------------------------------------------------------- :101: (p5) Found by Achim Flammenkamp in August 1994. The name was suggested by Bill Gosper, noting that the phase shown below displays the period in binary. ....**......**.... ...*.*......*.*... ...*..........*... **.*..........*.** **.*.*..**..*.*.** ...*.*.*..*.*.*... ...*.*.*..*.*.*... **.*.*..**..*.*.** **.*..........*.** ...*..........*... ...*.*......*.*... ....**......**.... :1-2-3: (p3) Found by Dave Buckingham, August 1972. This is one of only three essentially different p3 {oscillator}s with only three cells in the {rotor}. The others are {stillater} and {cuphook}. ..**...... *..*...... **.*.**... .*.*..*... .*....*.** ..***.*.** .....*.... ....*..... ....**.... :1-2-3-4: (p4) See also {Achim's p4}. .....*..... ....*.*.... ...*.*.*... ...*...*... **.*.*.*.** *.*.....*.* ...*****... ........... .....*..... ....*.*.... .....*..... :14-ner: = {fourteener} :2 eaters: = {two eaters} :4-8-12 diamond: The following {pure glider generator}. ....****.... ............ ..********.. ............ ************ ............ ..********.. ............ ....****.... :4 boats: (p2) ...*.... ..*.*... .*.**... *.*..**. .**..*.* ...**.*. ...*.*.. ....*... :4F: = {Fast Forward Force Field} :Achim's p144: (p144) This was found (minus the blocks shown below) on a cylinder of width 22 by Achim Flammenkamp in July 1994. Dean Hickerson reduced it to a finite form using {figure-8}s the same day. The neater finite form shown here - replacing the figure-8s with blocks - was found by David Bell in August 1994. See {factory} for a use of this oscillator. **........................** **........................** ..................**........ .................*..*....... ..................**........ ..............*............. .............*.*............ ............*...*........... ............*..*............ ............................ ............*..*............ ...........*...*............ ............*.*............. .............*.............. ........**.................. .......*..*................. ........**.................. **........................** **........................** :Achim's p16: (p16) Found by Achim Flammenkamp, July 1994. .......**.... .......*.*... ..*....*.**.. .**.....*.... *..*......... ***.......... ............. ..........*** .........*..* ....*.....**. ..**.*....*.. ...*.*....... ....**....... :Achim's p4: (p4) Dave Buckingham found this in a less compact form (using two halves of {sombreros}) in 1976. The form shown here was found by Achim Flammenkamp in 1988. The {rotor} is two copies of the rotor of {1-2-3-4}, so the oscillator is sometimes called the "dual 1-2-3-4". ..**...**.. .*..*.*..*. .*.**.**.*. **.......** ..*.*.*.*.. **.......** .*.**.**.*. .*..*.*..*. ..**...**.. :Achim's p5: = {pseudo-barberpole} :Achim's p8: (p8) Found by Achim Flammenkamp, July 1994. .**...... *........ .*...*... .*...**.. ...*.*... ..**...*. ...*...*. ........* ......**. :acorn: (stabilizes at time 5206) A {methuselah} found by Charles Corderman. .*..... ...*... **..*** :A for All: (p6) Found by Dean Hickerson in March 1993. ....**.... ...*..*... ...****... .*.*..*.*. *........* *........* .*.*..*.*. ...****... ...*..*... ....**.... :agar: Any pattern covering the whole plane that is periodic in both space and time. The simplest (nonempty) agar is the {stable} one extended by the known {spacefiller}s. For some more examples see {chicken wire}, {houndstooth agar}, {onion rings}, {squaredance} and {Venetian blinds}. Tiling the plane with the pattern O......O produces another interesting example: a p6 agar which has a phase of {density} 3/4, which is the highest yet obtained for any phase of an oscillating pattern. :aircraft carrier: (p1) This is the smallest {still life} that has more than one {island}. **.. *..* ..** :airforce: (p7) Found by Dave Buckingham in 1972. The rotor consists of two copies of that used in the {burloaferimeter}. .......*...... ......*.*..... .......*...... .............. .....*****.... ....*.....*.** ...*.**...*.** ...*.*..*.*... **.*...**.*... **.*.....*.... ....*****..... .............. ......*....... .....*.*...... ......*....... :AK47 reaction: The following reaction (found by Rich Schroeppel and Dave Buckingham) in which a honey farm predecessor, catalysed by an eater and a block, reappears at another location 47 generations later, having produced a glider and a traffic light. This is the basis of a very small (but {pseudo}) p94 glider gun found by Paul Callahan in July 1994, and was in 1990 the basis for the Dean Hickerson's construction of the first {true} p94 gun. (This latter gun was enormous, and has now been superceded by comparatively small {Herschel loop} guns.) .....*.... ....*.*... ...*...*.. ...*...*.. ...*...*.. ....*.*... .....*.... .......... ..**...... ...*...... ***.....** *.......** :Al Jolson: = {Jolson} :almosymmetric: (p2) Found in 1971. ....*.... **..*.*.. *.*...... .......** .*....... *......*. **.*.*... .....*... :antlers: = {moose antlers} :ants: (p5 wick) The standard form is shown below. It is also possible for any ant to be displaced by one or two cells relative to either or both of its neighbouring ants. Dean Hickerson found {fencepost}s for both ends of this wick in October 1992 and February 1993. See {electric fence}, and also {wickstretcher}. **...**...**...**...**...**...**...**...**.. ..**...**...**...**...**...**...**...**...** ..**...**...**...**...**...**...**...**...** **...**...**...**...**...**...**...**...**.. :anvil: The following {induction coil}. .****. *....* .***.* ...*.** :ark: A pair of mutually stabilizing {switch engine}s. The archetype is {Noah's ark}. :arm: A long extension hanging off from the main body of a {spaceship} or {puffer} perpendicular to the direction of travel. A lot of known spaceships, particularly c/3 ones, have multiple arms. This is an artefact of the search methods used to find such spaceships, rather than an indication of what a "typical" spaceship might look like. :ash: The ({stable} or oscillating) debris left by a random reaction. Experiments show that for random {soup}s with moderate initial densities (say 0.25 to 0.5) the resulting ash has a density of about 0.0287. (This is, of course, based on what happens in finite fields. In infinite fields the situation may conceivably be different in the long run because of the effect of certain initially very rare objects such as {replicator}s.) :aVerage: (p5) Found by Dave Buckingham, 1973. ...**........ ....***...... ..*....*..... .*.****.*.... .*.*....*..*. **.***..*.*.* .*.*....*..*. .*.****.*.... ..*....*..... ....***...... ...**........ :B: = {B-heptomino} :babbling brook: Any {oscillator} whose {rotor} consists of a string of cells each of which is adjacent to exactly two other rotor cells, except for the endpoints which are adjacent to only one other rotor cell. Compare {muttering moat}. Examples include the {beacon}, the {great on-off}, the {light bulb} and the {spark coil}. The following less trivial example (by Dean Hickerson, August 1997) is the only one known with more than four cells in its rotor. It is p4 and has a 6-cell rotor. .......*........ .....***....**.. ....*...**..*... .*..*.**..*.*... *.*.*....**..**. .**..**....*.*.* ...*.*..**.*..*. ...*..**...*.... ..**....***..... ........*....... :backrake: Another term for a backwards {rake}. For an example see {total aperiodic}. :backward glider: A {glider} which moves at least partly in the opposite direction to the {puffer}(s) or {spaceship}(s) under consideration. :baker: (c p4 fuse) A {fuse} by Keith McClelland. ..............** .............*.* ............*... ...........*.... ..........*..... .........*...... ........*....... .......*........ ......*......... .....*.......... ....*........... ...*............ ***............. .*.............. :baker's dozen: (p12) A {loaf} {hassle}d by two {block}s and two {caterer}s. The original form (using p4 and p6 oscillators to do the hassling) was found by Robert Wainwright in August 1989. **.........**.......... ****.*.....**.......... *.*..***............... ...........*........... ....**....*.*.......... ....*.....*..*....*.... ...........**....**.... ....................... ...............***..*.* ..........**.....*.**** ..........**.........** :bakery: (p1) A common formation of two bi-loaves. ....**.... ...*..*... ...*.*.... .**.*...*. *..*...*.* *.*...*..* .*...*.**. ....*.*... ...*..*... ....**.... :barberpole: Any p2 oscillator in the infinite sequence {bipole}, {tripole}, {quadpole}, {pentapole}, {hexapole}, {heptapole} ... (It wasn't my idea to suddenly change from Latin to Greek.) This sequence of oscillators was found by the MIT group in 1970. The term is also used (usually in the form "barber pole") to describe other extensible sections of oscillators or spaceships, especially those (usually of period 2) in which all generations look alike except for a translation and/or rotation/reflection. :barberpole intersection: = {quad} :barber's pole: = {barberpole} :barge: (p1) .*.. *.*. .*.* ..*. :basic shuttle: = {queen bee shuttle} :beacon: (p2) The third most common {oscillator}. Found by Conway, March 1970. **.. *... ...* ..** :beacon maker: (c p8 fuse) ..............** .............*.* ............*... ...........*.... ..........*..... .........*...... ........*....... .......*........ ......*......... .....*.......... ....*........... ...*............ ***............. ..*............. ..*............. :beehive: (p1) The second most common {still life}. .**. *..* .**. :beehive and dock: (p1) ...**. ..*..* ...**. ...... .****. *....* **..** :beehive on big table: = {beehive and dock} :beehive pusher: = {hivenudger} :beehive with tail: (p1) .**... *..*.. .**.*. ....*. ....** :belly spark: The spark of a {MWSS} or {HWSS} other than the {tail spark}. :bent keys: (p3) Found by Dean Hickerson, August 1989. See also {odd keys} and {short keys}. .*........*. *.*......*.* .*.**..**.*. ....*..*.... ....*..*.... :B-heptomino: (stabilizes at time 148) This is a very common pattern. It often arises with the cell at top left shifted one space to the left, which does not affect the subsequent evolution. B-heptominoes acquired particular importance in 1996 due to Dave Buckingham's work on {B track}s - see in particular {My Experience with B-heptominos in Oscillators}. *.** ***. .*.. :B-heptomino shuttle: = {twin bees shuttle} :bi-block: (p1) The smallest {pseudo still life}. **.** **.** :bi-boat: = {boat-tie} :biclock: The following {pure glider generator}. ..*.... **..... ..**... .*...*. ...**.. .....** ....*.. :big beacon: = {figure-8} :big fish: = {HWSS} :big glider: (c/4 diagonally, p4) This was found by Dean Hickerson in December 1989 and was the first known diagonal spaceship other than the {glider}. ...***............ ...*..***......... ....*.*........... **.......*........ *.*....*..*....... *........**....... .**............... .*..*.....*.**.... .*.........**.*... ...*.*......**..*. ....**.*....**...* ........*.......*. .......****...*.*. .......*.**...**** ........*...**.*.. .............**... .........*.***.... ..........*..*.... :big S: (p1) ....**. ...*..* ...*.** **.*... *..*... .**.... :big table: = {dock} :billiard table configuration: Any {oscillator} in which the {rotor} is enclosed within the {stator}. Examples include {airforce}, {cauldron}, {clock II}, {Hertz oscillator}, {negentropy}, {pinwheel}, {pressure cooker} and {scrubber}. :bi-loaf: This term has been used in at least three different senses. A bi-loaf can be half a {bakery}: .*..... *.*.... *..*... .**.*.. ...*.*. ...*..* ....**. or it can be the following much less common {still life}: ..*.... .*.*... *..*... .**.**. ...*..* ...*.*. ....*.. or the following {pure glider generator}: ..*. .*.* *..* .**. *..* *.*. .*.. :bipole: (p2) The {barberpole} of length 2. **... *.*.. ..... ..*.* ...** :bi-pond: (p1) .**.... *..*... *..*... .**.**. ...*..* ...*..* ....**. :bi-ship: = {ship-tie} :bit: A live {cell}. :biting off more than they can chew: = {eater-bound pond} :Black&White: = {Immigration} :blasting cap: The {pi-heptomino} (after the shape at generation 1). A term used at MIT and still occasionally encountered. :blinker: (p2) The smallest and most common {oscillator}. Found by Conway, March 1970. *** :blinkers bit pole: (p2) Found by Robert Wainwright, June 1977. .....** ***.*.* ....... .*.*..* *....*. **...*. :blinker ship: A {growing spaceship} in which the wick consists of a line of {blinker}s. An example by Paul Schick based on his {Schick engine} is shown below. Here the front part is p12 and moves at c/2, while the back part is p26 and moves at 6c/13. Every 156 generations 13 blinkers are created and 12 are destroyed, so the wick becomes one blinker longer. ..........****............. ..........*...*............ ..........*................ .**........*..*............ **.**...................... .****...*.................. ..**...*.**........*....*** ......*...*........*....*.* ..**...*.**........*....*** .****...*.................. **.**...................... .**........*..*............ ..........*................ ..........*...*............ ..........****............. :block: (p1) The most common {still life}. ** ** :blockade: (p1) A common formation of four blocks. The final form of {lumps of muck}. **..................... **..................... ....................... ....................... .**.................**. .**.................**. ....................... ....................... .....................** .....................** :block and dock: (p1) ...**. ...**. ...... .****. *....* **..** :block and glider: (stabilizes at time 106) **.. *.*. ..** :blocker: (p8) Found by Robert Wainwright. See also {filter}. ......*.*. .....*.... **..*....* **.*..*.** ....**.... :block on big table: = {block and dock} :block on table: (p1) ..** ..** .... **** *..* :blonk: A {block} or a {blinker}. This term is mainly used in the context of {sparse Life} and was coined by Rich Schroeppel in September 1992. :boat: (p1) The only 5-pixel {still life}. **. *.* .*. :boat-bit: A binary digit represented by the presence of a {boat} next to a {snake} (or other suitable object, such as an {aircraft carrier}). The bit can be toggled by a {glider} travelling along a certain path. A correctly timed glider on a crossing path can detect whether the transition was from 1 to 0 (in which case the crossing glider is deleted) or from 0 to 1 (in which case it passes unharmed). Three gliders therefore suffice for a non-destructive read. The mechanisms involved are shown in the diagram below. Here the bit is shown in state 0. It is about to be set to 1 and the switched back to 0 again. The first crossing glider will survive, but the second will be destroyed. (In January 1997 David Bell found a method of reading the bit while setting it to 0. A {MWSS} is fired at the boat-bit. If it is already 0 then the MWSS passes unharmed, but if it is 1 then the boat and the MWSS are destroyed and, with the help of a {eater1}, converted into a glider which travels back along exactly the same path that is used by the gliders that toggle the boat-bit.) ......*.................. .......*................. .....***................. ......................... ......................... ......................... ......................... ......................... ......................... ......................... ................*........ ..............*.*........ ..........**...**........ ...........**............ ..........*..........*.** .....................**.* ......................... ......................... ......................... ......................... ......................... .*....................... .**...................... *.*...................... :boat maker: (c p4 fuse) ................** ...............*.* ..............*... .............*.... ............*..... ...........*...... ..........*....... .........*........ ........*......... .......*.......... ......*........... .....*............ *****............. ....*............. ....*............. ....*............. ....*............. :boat on boat: = {boat-tie} :boat-ship-tie: = {ship tie boat} :boatstretcher: Any {wickstretcher} that stretches a boat. The first one was found by Hartmut Holzwart in June 1993. The following example is by Noam Elkies (February 1996) and uses Tim Coe's {swan}. Note that in any boatstretcher the point of the boat can be removed to get a tubstretcher. ............**.......... ***.........*.*......... *..***......*.........*. .*.*................**.* ......*....**..*...**..* ....*......**..*.**..*.. ......*.**.*...*****.... ...............**....... .......*..******........ ........*******......... ..........***........... ........................ .............*.......... ............*.*......... .............**......... :boat-tie: (p1) The name is a pun on "bow tie". .*.... *.*... .**... ...**. ...*.* ....*. :bookend: The following {induction coil}. It is generation 1 of {century}. ..** *..* ***. :bookends: (p1) **...** *.*.*.* ..*.*.. .**.**. :boss: (p4) Found by Dave Buckingham, 1972. .....*..... ....*.*.... ....*.*.... ...**.**... ..*.....*.. .*.*.*.*.*. .*.*...*.*. **.*...*.** *..*.*.*..* ..*.....*.. ...**.**... ....*.*.... ....*.*.... .....*..... :bottle: (p8) Found by Achim Flammenkamp in August 1994. The name is a back-formation from {ship in a bottle}. ....**......**.... ...*..*....*..*... ...*.*......*.*... .**..***..***..**. *......*..*......* *.**..........**.* .*.*..........*.*. ...**........**... .................. .................. ...**........**... .*.*..........*.*. *.**..........**.* *......*..*......* .**..***..***..**. ...*.*......*.*... ...*..*....*..*... ....**......**.... :bounding box: The smallest rectangular array of cells that contains the whole of a given pattern. For {oscillator}s and {gun}s this usually is meant to include all phases of the pattern, but excludes, in the case of guns, the outgoing stream(s). :bow tie: = {boat-tie} :brain: (c/3 orthogonally, p3) Found by David Bell, May 1992. .***.........***. *.*.**.....**.*.* *.*.*.......*.*.* .*.**.**.**.**.*. .....*.*.*.*..... ...*.*.*.*.*.*... ..**.*.*.*.*.**.. ..***..*.*..***.. ..**..*...*..**.. .*....**.**....*. .*.............*. :breeder: Any pattern whose {population} grows at a quadratic rate, although it is usual to exclude {spacefiller}s. It is easy to see that this is the fastest possible growth rate. The term is also sometimes used to mean specifically the breeder created by Bill Gosper's group at MIT, which was the first known pattern exhibiting superlinear growth. There are four basic types of breeder, known as MMM, MMS, MSM and SMM (where M=moving and S=stationary). Typically an MMM breeder is a {rake} {puffer}, an MMS is a puffer producing puffers which produce stationary objects ({still life}s and/or {oscillator}s), an MSM breeder is a {gun} puffer and an SMM breeder is a rake gun. There are, however, less obvious variants of these types. The original breeder was of type MSM (a p64 puffer puffing p30 glider guns). The known breeder with the smallest initial population is {mosquito5}. :bridge: A term used in naming certain {still life}s (and the {stator} part of certain {oscillator}s). It indicates that the object consists of two smaller objects joined edge to edge, as in {snake bridge snake}. :broth: = {soup} :BTC: = {billiard table configuration} :B track: A {track} for {B-heptomino}es. The term is more-or-less synonymous with {Herschel track}, since a B-heptomino becomes a Herschel plus a block in twenty generations. :buckaroo: A {queen bee shuttle} stabilized at one end by an eater in such a way that it can turn a glider, as shown below. This was found by Dave Buckingham in the 1970s. The name is due to Bill Gosper. ..*..................... *.*..................... .**..................... ...........*............ .........*.*............ ........*.*............. .......*..*...........** ........*.*...........** ...**....*.*............ ..*.*......*............ ..*..................... .**..................... :bullet heptomino: Generation 1 of the {T-tetromino}. .*. *** *** :bun: The following {induction coil}. By itself this is a common {predecessor} of the {honey farm}. See also {cis-mirrored R-bee}. .**. *..* .*** :bunnies: (stabilizes at time 17332) This is a {parent} of {rabbits} and was found independently by Robert Wainwright and Andrew Trevorrow. *.....*. ..*...*. ..*..*.* .*.*.... :burloaf: = {loaf} :burloaferimeter: (p7) Found by Dave Buckingham in 1972. See also {airforce}. ....**.... .....*.... ....*..... ...*.***.. ...*.*..*. **.*...*.* **.*....*. ....****.. .......... ....**.... ....**.... :bushing: That part of the {stator} of an {oscillator} which is adjacent to the {rotor}. Compare {casing}. :butterfly: The following pattern, or the formation of two beehives that it evolves into after 33 generations. (Compare {teardrop}, where the beehives are five cells closer together.) *... **.. *.*. .*** :by flops: (p2) Found by Robert Wainwright. ...*.. .*.*.. .....* *****. .....* .*.*.. ...*.. :c: = {speed of light} :CA: = {cellular automaton} :caber tosser: Any pattern whose {population} is asymptotic to c.log(t) for some constant c, and which contains a {glider} (or other {spaceship}) bouncing between a slower receding spaceship and a fixed {reflector} which emits a spaceship (in addition to the reflected one) whenever the bouncing spaceship hits it. As the receding spaceship gets further away the bouncing spaceship takes longer to complete each cycle, and so the extra spaceships emitted by the reflector are produced at increasingly large intervals. More precisely, if v is the speed of the bouncing spaceship and u the speed of the receding spaceship, then each interval is (v+u)/(v-u) times as long as the previous one. The population at time t is therefore n.log(t)/log((v+u)/(v-u))+O(1), where n is the population of one of the extra spaceships (assumed constant). The first caber tosser was built by Dean Hickerson in August 1994. :Cambridge pulsar CP 48-56-72: = {pulsar} (The numbers refer to the populations of the three phases. The Life pulsar was indeed discovered at Cambridge, like the first real pulsar a few years earlier.) :Canada goose: (c/4 diagonally, p4) Found by Jason Summers, January 1999. It consists of a {glider} plus a {tagalong}. At the time of its discovery it was the smallest known diagonal {spaceship} other than the glider, but this record has since been beaten (see {Orion}). ***.......... *.........**. .*......***.* ...**..**.... ....*........ ........*.... ....**...*... ...*.*.**.... ...*.*..*.**. ..*....**.... ..**......... ..**......... :candelabra: (p3) By Charles Trawick. See also the note under {cap}. ....**....**.... .*..*......*..*. *.*.*......*.*.* .*..*.****.*..*. ....*.*..*.*.... .....*....*..... :candlefrobra: (p3) Found by Robert Wainwright in November 1984. .....*.... .*.**.*.** *.*...*.** .*....*... .....**... The following diagram shows that a pair of these can act in some ways like {killer toads}. See also {snacker}. ....*...........*.... **.*.**.*...*.**.*.** **.*...*.*.*.*...*.** ...*....*...*....*... ...**...........**... ..................... ..................... .........***......... .........*..*........ .........*........... .........*...*....... .........*...*....... .........*........... ..........*.*........ :canoe: (p1) ...** ....* ...*. *.*.. **... :cap: The following {induction coil}. It can also be easily be stabilized to form a p3 oscillator - see {candelabra} for a slight variation on this. .**. *..* **** :carnival shuttle: (p12) Found by Robert Wainwright in September 1984 (using {MW emulator}s at the end, rather than {monogram}s). .................................*...* **...**..........................***** .*.*.*...*..*......**...*..*.......*.. .**.**..**...**....**..**...**....*.*. .*.*.*...*..*......**...*..*.......*.. **...**..........................***** .................................*...* :carrier: = {aircraft carrier} :casing: That part of the {stator} of an {oscillator} which is not adjacent to the {rotor}. Compare {bushing}. :catacryst: A 58-cell quadratic growth pattern found by Nick Gotts in April 2000. This is the smallest known pattern with superlinear growth, beating the record previously held by {teeth}. Catacryst consists of three {ark}s plus a glider-producing {switch engine}. It produces a block-laying switch engine every 47616 generations. Each block-laying switch engine has only a finite life, but the length of this life increases linearly with each new switch engine, so that the pattern overall grows quadratically, as an unusual type of MMS {breeder}. :catalyst: An object that participates in a reaction but emerges from it unharmed. The term is mostly applied to {still life}s, but can also be used of {oscillator}s, {spaceship}s, etc. The still lifes and oscillators which form a {conduit} are examples of catalysts. :caterer: (p3) Found by Dean Hickerson, August 1989. Compare with {jam}. In terms of its minimum {population} of 12 this is the smallest p3 {oscillator}. See also {double caterer} and {triple caterer}. ..*..... *...**** *...*... *....... ...*.... .**..... More generally, any oscillator which serves up a {bit} in the same manner may be referred to as a ceterer. :Catherine wheel: = {pinwheel} :cauldron: (p8) Found in 1971 independently by Don Woods and Robert Wainwright. Compare with {Hertz oscillator}. .....*..... ....*.*.... .....*..... ........... ...*****... *.*.....*.* **.*...*.** ...*...*... ...*...*... ....***.... ........... ....**.*... ....*.**... :cavity: (p2) **...... .*...... .*.**... ..*..*.. .....*.. ....*... .....*** .......* :cell: The fundamental unit of space in the Life universe. The term is often used to mean a live cell - the sense is usually clear from the context. :cellular automaton: A certain class of mathematical objects of which {Life} is an example. A cellular automaton consists of a number of things. First there is a positive integer n which is the dimension of the cellular automaton. Then there is a finite set of states S, with at least two members. A state for the whole cellular automaton is obtained by assigning an element of S to each point of the n-dimensional lattice Z^n (where Z is the set of all integers). The points of Z^n are usually called cells. The cellular automaton also has the concept of a neighbourhood. The neighbourhood N of the origin is some finite (nonempty) subset of Z^n. The neighbourhood of any other cell is obtained in the obvious way by translating that of the origin. Finally there is a transition rule, which is a function from S^N to S (that is to say, for each possible state of the neighbourhood the transition rule specifies some cell state). The state of the cellular automaton evolves in discrete time, with the state of each cell at time t+1 being determined by the state of its neighbourhood at time t, in accordance with the transition rule. There are some variations on the above definition. It is common to require that there be a quiescent state, that is, a state such that if the whole universe is in that state at generation 0 then it will remain so in generation 1. (In Life the OFF state is quiescent, but the ON state is not.) Other variations allow spaces other than Z^n, neighbourhoods that vary over space and/or time, probabilistic or other non-deterministic transistion rules, etc. It is common for the neighbourhood of a cell to be the 3x...x3 (hyper)cube centred on that cell. (This includes those cases where the neighbourhood might more naturally be thought of as a subset of this cube.) This is known as the Moore neighbourhood. :centinal: (p100) Found by Bill Gosper. This combines the mechanisms of the p46 and p54 shuttles (see {twin bees shuttle} and {p54 shuttle}). **................................................** .*................................................*. .*.*.....................**.....................*.*. ..**........*............**............**.......**.. ...........**..........................*.*.......... ..........**.............................*.......... ...........**..**......................***.......... .................................................... .................................................... .................................................... ...........**..**......................***.......... ..........**.............................*.......... ...........**..........................*.*.......... ..**........*............**............**.......**.. .*.*.....................**.....................*.*. .*................................................*. **................................................** :century: (stabilizes at time 103) This is a common pattern which evolves into three {block}s and a {blinker}. In June 1996 Dave Buckingham built a neat p246 glider {gun} using a century as the engine. See also {bookend} and {diuresis}. ..** ***. .*.. :chemist: (p5) .......*....... .......***..... ..........*.... .....***..*..** ....*.*.*.*.*.* ....*...*.*.*.. .**.*.....*.**. ..*.*.*...*.... *.*.*.*.*.*.... **..*..***..... ....*.......... .....***....... .......*....... :C-heptomino: Name given by Conway to the following {heptomino}, a less common variant of the {B-heptomino}. .*** ***. .*.. :Cheshire cat: A block {predecessor} by C. R. Tompkins that unaccountably appeared both in Scientific American and in {Winning Ways}. See also {grin}. .*..*. .****. *....* *.**.* *....* .****. :chicken wire: A type of {stable} {agar} of {density} 1/2. The simplist version is formed from the tile: **.. ..** But the "wires" can have length greater than two and need not all be the same. For example: **...****..... ..***....***** :cigar: = {mango} :cis-beacon on anvil: (p2) ...**. ....*. .*.... .**... ...... .****. *....* .***.* ...*.** :cis-beacon on table: (p2) ..** ...* *... **.. .... **** *..* :cis-boat with tail: (p1) .*... *.*.. **.*. ...*. ...** :cis fuse with two tails: (p1) See also {pulsar quadrant}. ...*.. .***.. *...** .*..*. ..*.*. ...*.. :cis-mirrored R-bee: (p1) .**.**. *.*.*.* *.*.*.* .*...*. :cis snake: = {canoe} :clean: Opposite of {dirty}. A reaction which produces a small number of different products which are desired or which are easily deleted is said to be clean. For example, a {puffer} which produces just one object per period is clean. Clean reactions are useful because they can be used as building blocks in larger constructions. When a {fuse} is said to be clean, or to burn cleanly, this usually means that no debris at all is left behind. :clock: (p2) Found by Simon Norton, May 1970. This is the fifth or sixth most common {oscillator}, being about as frequent as the {pentadecathlon}, but much less frequent than the {blinker}, {toad}, {beacon} or {pulsar}. But it's surprisingly rare considering its small size. ..*. *.*. .*.* .*.. :clock II: (p4) Compare with {pinwheel}. ......**.... ......**.... ............ ....****.... **.*....*... **.*..*.*... ...*..*.*.** ...*.*..*.** ....****.... ............ ....**...... ....**...... :cloud of smoke: = {smoke} :cloverleaf: This name was given by Robert Wainwright to his p2 oscillator {washing machine}. But Achim Flammenkamp also gave this name to {Achim's p4}. :cluster: Any pattern in which each live cell is connected to every other live cell by a path that does not pass through two consecutive dead cells. This sense is due to Nick Gotts, but the term has also been used in other senses, often imprecise. :CNWH: Conweh, creator of the Life universe. :Coe ship: (c/2 ortogonally, p16) A {puffer engine} discovered by Tim Coe in October 1995. ....****** ..**.....* **.*.....* ....*...*. ......*... ......**.. .....****. .....**.** .......**. :Coe's p8: (p8) Found by Tim Coe in August 1997. **.......... **..**...... .....**..... ....*..*.... .......*..** .....*.*..** :colorized Life: A {cellular automaton} which is the same as Life except for the use of a number of different ON states ("colours"). All ON states behave the same for the purpose of applying the Life rule, but additional rules are used to specify the colour of the resulting ON cells. Examples are {Immigration} and {QuadLife}. :complementary blinker: = {fore and back} :compression: = {repeat time} :conduit: Any arrangement of {still life}s and/or {oscillator}s which move an active object to another location, perhaps also transforming it into a different active object at the same time, but without leaving any permanent debris (except perhaps gliders, or other spaceships) and without any of the still lifes or oscillators being permanently damaged. Probably the most important conduit is the following remarkable one (Dave Buckingham, July 1996) in which a {B-heptomino} is transformed into a {Herschel} in 59 generations. .........**.* *.**......*** **.*.......*. ............. .........**.. .........**.. :confused eaters: (p4) Found by Dave Buckingham before 1973. *.......... ***........ ...*....... ..*........ ..*..*..... .....*..... ...*.*..... ...**..**.. .......*.*. .........*. .........** :converter: A {conduit} in which the input object is not of the same type as the output object. This term tends to be preferred when either the input object or the output object is a {spaceship}. The following diagram shows a p8 {pi-heptomino}-to-{HWSS} converter. This was originally found by Dave Buckingham in a larger form (using a {figure-8} instead of the {boat}). The improvement shown here is by Bill Gosper (August 1996). Dieter Leithner has since found (much larger) oscillators of periods 44, 46 and 60 to replace the {Kok's galaxy}. .*.*..*........ .***.*.**...... *......*.....*. .*.....**...*.* .............** **.....*....... .*......*...... **.*.***....... ..*..*.*....... ............*** ............*.* ............*.* :convoy: A collection of {spaceship}s all moving in the same direction at the same speed. :Corder engine: = {switch engine} :Cordership: Any {spaceship} based on {switch engine}s. These necessarily move at a speed of c/12 diagonally with a period of 96 (or a multiple thereof), and the first was found by Dean Hickerson in April 1991. Corderships are by far the slowest spaceships yet constructed, although arbitrarily slow spaceships are known to exist (see {universal constructor}). Hickerson's original Cordership used 13 switch engines. He soon reduced this to 10, and in August 1993 to 7. In July 1998 he reduced it to just 6, and this is shown below. ..........................................**................... ......................................**...*................... ...........................***.......*......*.................. ..............................***.....*...*****................ ..............................***......*...*................... ...............................*...........*..*................ ............................................**.......**........ .....................................................**........ ............................................................... ............................................................... ............................................................... ............................................................... ....................***........................................ ....................***..................*..................... ........................................*.*..................** ....................*.**................*..*.................** ....................*...*................**.................... ......................***...................................... .....................................**........................ .....................................**........................ ............................................................... ............................................................... ..............................*................................ .....*.......................*.*.........................*..... .****.**.....***.............*.*.....................****.**... **.***.**....***..............*.....................**.***.**.. .*.***.*.......**....................................*.***.*... ..*...****....**......................................*...****. .....**.***..............................................**.*** ......*****.........**....................................***** .......*............**.....................................*... ............................................................... ............................................................... ............................................................... ...........................................*................... ..........................................***.................. ..........................***.............*..*................. ......................*....**.............***.................. ....................****..................***.................. ............*......**.**.................*.**.*................ .........**....*..*.*.....................*..***............... ....**.....**...*.........................****.**.............. ....**.......*.**...***..**................*.***............... .....................**..**..................***............... ..............................................**............... ............................................................... ............................................................... .............................*................................. .........................****.**....*...**.***................. ............**..........**.***.**...**...*****................. ............**...........*.***.*....***...***.................. ..........................*...****....**....................... .............................**.***............................ ..............................*****............................ ...............................*............................... ............................................................... ............................................................... ....................**......................................... ....................**......................................... :cousins: (p3) This contains two copies of the {stillater} {rotor}. .....*.**.... ...***.*.*... *.*......*... **.**.**.*.** ...*.*....*.* ...*.*.***... ....**.*..... :cover: The following {induction coil}. See {scrubber} for an example of its use. ....* ..*** .*... .*... **... :covered table: = {cap} :cow: (c p8 fuse) **.......**..**..**..**..**..**..**..**..**..**..**..**..... **....*.***..**..**..**..**..**..**..**..**..**..**..**...** ....**.*.................................................*.* ....**...*************************************************.. ....**.*..................................................*. **....*.***..**..**..**..**..**..**..**..**..**..**..**..**. **.......**..**..**..**..**..**..**..**..**..**..**..**..... :CP pulsar: = {pulsar} :cross: (p3) Found by Robert Wainwright in October 1989. In February 1993 Hartmut Holzwart discovered that arbitrarily large analogues of this also exist. ..****.. ..*..*.. ***..*** *......* *......* ***..*** ..*..*.. ..****.. :crowd: (p3) Found by Dave Buckingham in January 1973. ...........*.. .........***.. .....**.*..... .....*...*.... .......**.*... ...****...*... *.*.....*.*.** **.*.*.....*.* ...*...****... ...*.**....... ....*...*..... .....*.**..... ..***......... ..*........... :crown: The p12 part of the following p12 {oscillator}, where it is {hassle}d by {caterer}, a {jam} and a {HW emulator}. This oscillator was found by Noam Elkies in January 1995. ..........*........... ..........*......*.... ...*....*...*...**.... ...**....***.......... .........***..***..*.* .*..***.........*.**** *.*.*...............** *..*.................. .**........**......... ......**.*....*.**.... ......*..........*.... .......**......**..... ....***..******..***.. ....*..*........*..*.. .....**..........**... :crucible: = {cauldron} :cuphook: (p3) Found by Rich Schroeppel, October 1970. This is one of only three essentially different p3 {oscillator}s with only three cells in the {rotor}. The others are {1-2-3} and {stillater}. ....**... **.*.*... **.*..... ...*..... ...*..*.. ....**.*. .......*. .......** The above is the original form, but it can be made more compact: ....**. ...*.*. ...*... **.*... **.*..* ...*.** ...*... ..**... :curl: = {loop} :dart: (c/3 ortogonally, p3) Found by David Bell, May 1992. .......*....... ......*.*...... .....*...*..... ......***...... ............... ....**...**.... ..*...*.*...*.. .**...*.*...**. *.....*.*.....* .*.**.*.*.**.*. :dead spark coil: (p1) Compare {spark coil}. **...** *.*.*.* ..*.*.. *.*.*.* **...** :density: The density of a pattern is the limit of the proportion of live cells in a (2n+1)x(2n+1) square centred on a particular cell as n tends to infinity, when this limit exists. (Note that it does not make any difference what cell is chosen as the centre cell. Also note that if the pattern is finite then the density is zero.) There are other definitions of density, but this one will do here. In 1994 Noam Elkies proved that the maximum density of a stable pattern is 1/2, which had been the conjectured value. See the paper listed in the bibliography. Marcus Moore provided a simpler proof in 1995, and in fact proves that a {still life} with an m x n {bounding box} has at most (mn+m+n)/2 cells. But what is the maximum average density of an oscillating pattern? The answer is conjectured to be 1/2 again, but this remains unproved. The best upper bound so far obtained is 8/13 (Hartmut Holzwart, September 1992). The maximum possible density for a phase of an oscillating pattern is also unknown. An example with a density of 3/4 is known (see {agar}), but densities arbitrarily close to 1 may perhaps be possible. :D-heptomino: = {Herschel} :diamond: = {tub} :diamond ring: (p3) Found by Dave Buckingham in 1972. ......*...... .....*.*..... ....*.*.*.... ....*...*.... ..**..*..**.. .*....*....*. *.*.**.**.*.* .*....*....*. ..**..*..**.. ....*...*.... ....*.*.*.... .....*.*..... ......*...... :diehard: Any pattern that vanishes, but only after a long time. The following example vanishes in 130 generations, which is probably the limit for patterns of 7 or fewer cells. Note that there is no limit for higher numbers of cells - e.g., for 8 cells we could have a glider heading towards an arbitrarily distant blinker. ......*. **...... .*...*** :dinner table: (p12) Found by Robert Wainwright in 1972. .*........... .***.......** ....*......*. ...**....*.*. .........**.. ............. .....***..... .....***..... ..**......... .*.*....**... .*......*.... **.......***. ...........*. :dirty: Opposite of {clean}. A reaction which produces a large amount of complicated junk which is difficult to control or use is said to be dirty. Many basic {puffer engine}s are dirty and need to be {tame}d by accompanying {spaceship}s in order to produce clean output. :diuresis: (p90) Found by David Eppstein in October 1998. His original stabilization used {pentadecathlon}s. The stabilization with complicated {still life}s shown here (in two slightly different forms) was found by Dean Hickerson the following day. The name is due to Bill Gosper (see {kidney}). .....**................**.... ......*................*..... ......*.*............*.*..... .......**............**...... ............................. ....**..................**... ....*.*..........**....*.*... .....*..........*.*.....*.... ..*.............**.........*. ..******........*.....******. .......*..............*...... ....**..................**... ....*....................*... .....*..................*.... ..***..*..............*..***. ..*..***........*.....***...* ...*............**.......***. ....**..........*.*.....*.... ......*..........**....*..**. ....**..................**.*. .*..*....................*... *.*.*..**............**..*... .*..*.*.*............*.*.**.. ....*.*................*..*.. .....**................**.... :dock: The following {induction coil}. .****. *....* **..** :domino: The 2-cell {polyomino}. A number of objects, such as the {HWSS} and {pentadecathlon}, produce domino {spark}s. :double-barrelled: Of a {gun}, emitting two streams of {spaceship}s (or {rake}s). The following diagram shows a double-barrelled p104 glider gun. This gun was found by Noam Elkies in March 1996 (except that Elkies used {blocker}s instead of {mold}s, the improvement being found by David Bell later the same month). .**.................................... .**.................*.................. ...................*.*............*.*.. ....................*............*..... **.......**.......................*..*. **.*.....**.......................*.*.* ...*.......................*.......*..* ...*.......................**.......**. *..*.................**.....*.......... .**..................*................. .....................***............... ....................................**. ....................................**. .**.................................... *..*................................... *.*.*................*.*....**.....**.. .*..*.................**....**.....**.* .....*............*...*...............* ..*.*............*.*..................* ..................*................*..* ....................................**. :double block reaction: A certain reaction that can be used to stabilize the {twin bees shuttle} (qv). This was discovered by David Bell in October 1996. The same reaction sometimes works in other situations, as shown in the following diagram where a pair of blocks eats an {R-pentomino} and a {LWSS}. .****.....**.... *...*......**.** ....*......*..** *..*............ ................ .............**. .............**. :double caterer: (p3) Found by Dean Hickerson, October 1989. Compare {caterer} and {triple caterer}. .....**...*........ ....*..*..***...... ....**.*.....*..... ......*.****.*..... ..***.*.*...*.**... .*..*..*...*..*.*.. *.*..*...*.**....*. .*..........**.***. ..**.**.**...*..... ...*...*.....*.***. ...*...*......**..* .................** :double ewe: (p3) Found by Robert Wainwright before September 1971. ......**............ .......*............ ......*............. ......**............ .........**......... ......***.*......... *.**.*.............. **.*.*.............. .....*...*.......... ....*...**....**.... ....**....**...*.... ..........*...*..... ..............*.*.** ..............*.**.* .........*.***...... .........**......... ............**...... .............*...... ............*....... ............**...... :double wing: = {moose antlers} :dove: The following {induction coil}. .**.. *..*. .*..* ..*** :down boat with tail: = {cis-boat with tail} :dragon: (c/6 orthogonally, p6) This {spaceship}, discovered by Paul Tooke in April 2000, was the first known c/6 spaceship. All other known c/6 spaceships are {flotilla}s involving at least two dragons. .............*..**......*..*** .....*...****.******....*..*** .*****....*....*....***....... *......**.*......**.***..*.*** .*****.***........****...*.*** .....*..*..............*...... ........**..........**.**..... ........**..........**.**..... .....*..*..............*...... .*****.***........****...*.*** *......**.*......**.***..*.*** .*****....*....*....***....... .....*...****.******....*..*** .............*..**......*..*** :drain trap: = {paperclip} :dual 1-2-3-4: = {Achim's p4} :early universe: Conway's somewhat confusing term for {sparse Life}. :eater: Any {still life} that has the ability to interact with certain patterns without suffering any permanent damage. (If it doesn't suffer even temporary damage then it may be referred to as a {rock}.) The {eater1} is a very common eater, and the term "eater" is often used specifically for this object. Other eaters include {eater2}, {eater3}, {eater4} and even the humble {block}. (In fact the block was the first known eater, being found capable of eating beehives from a {queen bee}.) Another useful eater is shown below, feasting on a glider. ...*..... ...*.*... ...**.... ......... .......** ...*...** ..*.*.... .*.*..... .*....... **....... :eater1: (p1) Usually simply called an {eater}, and also called a fishhook. Its ability to eat various objects was discovered by Bill Gosper in 1971. **.. *.*. ..*. ..** :eater2: (p1) This {eater} was found by Dave Buckingham in the 1970s. Mostly it works like the ordinary eater (see {eater1}) but with two slight differences that make it useful despite its size: it takes longer to recover from each bite and it acts like an eater in two directions. The first property means that, among other things, it can eat a {glider} in a position that would destroy a fishhook. This novel glider-eating action is occasionally of use in itself, and combined with the symmetry means that an eater2 can eat gliders along four different paths. An eater2 variant noticed by Stephen Silver in May 1998 that is useful for obtaining smaller {bounding box}es can be seen under {gliderless}. ...*.** .***.** *...... .***.** ...*.*. ...*.*. ....*.. :eater3: (p1) This large symmetric {eater}, found by Dave Buckingham, has a very different eating action from the {eater1} and {eater2}. The {loaf} can take bites out things, being flipped over in the process. The rest of the object merely flips it back again. .........**. ....**..*..* .*..*....*.* *.*.*.....*. .*..*.**.... ....*..*.... .....*....*. ......*****. ............ ........*... .......*.*.. ........*... :eater4: (p1) Another {eater} by Dave Buckingham, which he found in 1971, but did not recognize as an eater until 1975 or 1976. It can't eat {glider}s, but it can be used for various other purposes. The four NE-most centre cells regrow in a few generations after being destroyed by taking a bite out of something. ...**......... ...*.......... **.*.......... *..**......... .**....*...... ...*****...... ...*....**.... ....**..*..... ......*.*..... ......*.*.*..* .......**.**** .........*.... .........*.*.. ..........**.. :eater/block frob: (p4) Found by Dave Buckingham in 1976 or earlier. .**....... ..*....... ..*.*..... ...*.*.... .....**.** ........** ..**...... ...*...... ***....... *......... :eater-bound pond: (p3) Found by Peter Raynham, July 1972. *........... ***......... ...*........ ..**........ ...**....... ....**...... ...*..*..... ...*..**.... ....**.***.. ........*.*. ..........*. ..........** :eater-bound Z-hexomino: = {pentoad} :eater eating eater: = {two eaters} :eater plug: (p2) Found by Robert Wainwright, February 1973. .......* .....*** ....*... .....*.. ..*..*.. .*.**... .*...... **...... :eaters +: = {French kiss} :eaters plus: = {French kiss} :ecologist: (c/2 orthogonally, p20) This consists of the classic {puffer train} with a {LWSS} added to suppress the debris. See also {space rake}. ****.....**........ *...*...**.**...... *........****...... .*..*.....**....... ................... .....*.........**.. ...***........***** ..*...*.....*....** ..*....*****.....** ..**.*.****....**.. ....*...**.***..... .....*.*........... ................... ................... ****............... *...*.............. *.................. .*..*.............. :edge-repair spaceship: (c/3 orthogonally, p3) Any of a family of {spaceship}s whose left-hand edge can be used to {perturb} things, since it can often repair damage done to itself. Below are shown the two smallest and most useful members of this family, both found by David Bell in 1992. The usefulness of the edge-repair property wasn't recognised until July 1997. ..................................*..... ........*.......................***.***. .......****....................**......* ..*...*...**.**...........*...*..*...**. .****.....*..**..........****........... *...*.......*..*........*...*........... .*.*..*..................*.*..*......... .....*.......................*.......... :edge shooter: A {gun} which fires its gliders (or whatever) right at the edge of the pattern, so that it can be used to fire them closely parallel to others. This is useful for constructing complex guns. Compare {glider pusher}, which can in fact be used for making edge shooters. The following diagram shows a p46 edge shooter found by Paul Callahan in June 1994. **............**..*....**..**............. **............*.**......**.**............. ...............*......*.*................. ...............***....**.................. .......................................... ...............***....**.................. ...............*......*.*................. **............*.**......**................ **............**..*....**................. .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... ...............................***...***.. ..............................*...*.*...*. .............................*...**.**...* .............................*.**.....**.* ...............................*.......*.. .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... ...............................**.....**.. ...............................**.....**.. :edge spark: A {spark} at the side of a {spaceship} that can be used to {perturb} things as the spaceship passes by. :egg: = {non-spark} :E-heptomino: Name given by Conway to the following {heptomino}. .*** **.. .**. :electric fence: (p5) A stabilization of {ants}. Dean Hickerson, February 1993. ..........*................................................... .........*.*........................**........................ ..*....***.*.....*...................*...*..*......*........** .*.*..*....**...*.*..................*.***..***...*.*......*.* .*.*..*.**.......*....................*...**...*.*..*......*.. **.**.*.*.*****.....*..................**...*..*.*.**.**..**.. .*.*..*...*..*..*.......**...**...**....**.**..*.*..*.*.*..... .*..**....**......***.**...**...**...***.....****.***.*...**.. ..*..***..*..*.****...**...**...**...***.**..*....*.*....*..*. ...**...*.*..*.....**...**...**...**......*............*...**. .....**.*.**.*.**..*......................*........**.*....... .....*.**.*..*.**....*.................**.*.*................. ...........**.......**..................*..**................. ......................................*.*..................... ......................................**...................... :elevener: (p1) **.... *.*... ..*... ..***. .....* ....** :Elkies' p5: (p5) Found by Noam Elkies in 1997. .*....... *..***... ..*...... ...*.*..* ..**.**** ....*.... ....*.*.. .....**.. :emu: Dave Buckingham's term for a {Herschel loop} that does not emit {glider}s (and so is "flightless"). All known Herschel loops of periods 57, 58, 59 and 61 are emus. See also {Quetzal}. :emulator: Any one of three p4 oscillators that produce {spark}s similar to those produced by {LWSS}, {MWSS} and {HWSS}. See {LW emulator}, {MW emulator} and {HW emulator}. Larger emulators are also possible, but they require stabilizing objects to suppress their {non-spark}s and so are of little use. The emulators were discovered by Robert Wainwright in June 1980. :en retard: (p3) Found by Dave Buckingham, August 1972. .....*..... ....*.*.... **.*.*.*.** .*.*...*.*. *..*.*.*..* .**.....**. ...**.**... ...*.*.*... ....*.*.... ..*.*.*.*.. ..**...**.. :Enterprise: (c/4 diagonally, p4) Found by Dean Hickerson, March 1993. .......***........... .....*.**............ ....****............. ...**.....*.......... ..***..*.*.*......... .**...*.*..*......... .*.*.*****........... **.*.*...*........... *........**.......... .**..*...*.*......... ....**..*.**......*.. ...........**.....*** ............*..***..* ............*..*..**. .............*.**.... ............**....... ............**....... ...........*......... ............*.*...... ...........*..*...... .............*....... :Eureka: (p30) A {pre-pulsar} {shuttle} found by Dave Buckingham in August 1980. A variant is obtained by shifting the top half two spaces to either side. .*..............*. *.*....*.......*.* .*...**.**......*. .......*.......... .................. .................. .................. .......*.......... .*...**.**......*. *.*....*.......*.* .*..............*. :exposure: = {underpopulation} :extremely impressive: (p6) Found by Dave Buckingham, August 1976. ....**...... ...*.***.... ...*....*... **.*...**... **.*.....**. ....*****..* ..........** ......*..... .....*.*.... ......*..... :evolutionary factor: For an unstable pattern, the time to stabilization divided by the initial {population}. For example, the {R-pentomino} has an evolutionary factor of 220.6, while {bunnies} has an evolutionary factor of 1925.777... The term is no longer in use. :extra extra long: = {long^4} :extra long: = {long^3} :factory: Another word for {gun}, but not used in the case of glider guns. The term is also used for a pattern that repeatedly manufactures objects other than {spaceship}s or {rake}s. In this case the new objects do not move out of the way, and therefore must be used up in some way before the next one is made. The following shows an example of a p144 gun which consists of a p144 block factory whose output is converted into gliders by a p72 oscillator. (This gun is David Bell's improvement of the one Bill Gosper found in July 1994. The p72 oscillator is by Robert Wainwright, 1990, and the block factory is {Achim's p144} minus one of its stabilizing blocks.) .......................**........................** .......................**........................** .........................................**........ ........................................*..*....... .........................................**........ ................................................... ....................................***............ ....................................*.*............ .........**.........................***............ .........**.........................**............. ........*..*.......................***............. ........*..*.**....................*.*............. ........*....**....................***............. ..........**.**.................................... ...............................**.................. .....................**.......*..*................. .....................**........**.................. .................................................** .................................................** ................................................... ....**..................*.......................... **....****..........**..**.***..................... **..**.***..........**....****..................... ....*...................**......................... :familiar fours: Common patterns of four identical objects. The five commonest are {traffic light} (4 blinkers), {honey farm} (4 beehives), {blockade} (4 blocks), {fleet} (4 ships, although really 2 ship-ties) and {bakery} (4 loaves, although really 2 bi-loaves). :fanout: A mechanism that emits two or more objects of some type for each one that it receives. Typically the objects are {glider}s or {Herschel}s. :Fast Forward Force Field: The following reaction found by Dieter Leithner in May 1994. In the absence of the incoming LWSS the gliders would simply annihilate one another, but as shown they allow the LWSS to advance 11 spaces in the course of the next 6 generations. A neat illusion. See also {star gate}. (Leithner named the Fast Forward Force Field in honour of his favorite science fiction writer, the physicist Robert L. Forward.) .......*......*.. ........*......** ..**..***.....**. **.**............ ****.........*... .**.........**... ............*.*.. :father: = {parent} :featherweight spaceship: = {glider} :fencepost: Any pattern that stabilizes one end of a {wick}. :Fermat prime calculator: A pattern constructed by Jason Summers in January 2000 that exhibits {infinite growth} if and only if there are no Fermat primes greater than 65537. The question of whether or not it really does exhibit infinite growth is therefore equivalent to a well-known and long-standing unsolved mathematical problem. The pattern is based on Dean Hickerson's {primer}. :F-heptomino: Name given by Conway to the following {heptomino}. **.. .*.. .*.. .*** :figure-8: (p8) Found by Simon Norton in 1970. ***... ***... ***... ...*** ...*** ...*** :filter: Any {oscillator} used to delete some but not all of the {spaceship}s in a stream. An example is the {blocker}, which can be positioned so as to delete every other {glider} in a stream of period 8n+4, and can also do the same for {LWSS} streams. Other examples are the {MW emulator} and {T-nosed p4} (either of which can be used to delete every other LWSS in a stream of period 4n+2), the {fountain} (which does the same for {MWSS} streams) and a number of others, such as the p6 {pipsquirter}, the {pentadecathlon} and the p72 oscillator shown under {factory}. Another example, a p4 oscillator deleting every other HWSS in a stream of period 4n+2, is shown below. (The p4 oscillator here was found, with a slightly larger {stator}, by Dean Hickerson in November 1994.) ..........****............ ....**...******........... ****.**..****.**.......... ******.......**........... .****..................... .......................... ................**........ ..............*....*...... .......................... .............*.*..*.*..... ...........****.**.****... ........*.*....*..*....*.* ........**.**.*....*.**.** ...........*.*......*.*... ........**.*.*......*.*.** ........**.*..........*.** ...........*.*.****.*.*... ...........*.*......*.*... ..........**.*.****.*.**.. ..........*..***..***..*.. ............*..****..*.... ...........**.*....*.**... ...........*..*....*..*... ............*..*..*..*.... .............**....**..... :fish: A generic term for {LWSS}, {MWSS} and {HWSS}, or, more generally, for any {spaceship}. :fishhook: = {eater1} :fleet: (p1) A common formation of two ship-ties. ....**.... ....*.*... .....**... .......**. **.....*.* *.*.....** .**....... ...**..... ...*.*.... ....**.... :flip-flop: Any p2 {oscillator}. However, the term is also used in two more specific (and non-equivalent) senses: (a) any p2 oscillator whose two phases are mirror images of one another, and (b) any p2 oscillator in which all {rotor} cells die from {underpopulation}. In the latter sense it contrasts with {on-off}. The term has also been used even more specifically for the 12-cell flip-flop shown under {phoenix}. :flip-flops: Another name for the flip-flop shown under {phoenix}. :flipper: Any {oscillator} or {spaceship} that forms its mirror image halfway through its period. :flotilla: A {spaceship} composed of a number of smaller interacting spaceships. Often one or more of these is not a true spaceship and could not survive without the support of the others. The following example shows an {OWSS} escorted by two {HWSS}. ....****....... ...******...... ..**.****...... ...**.......... ............... ...........**.. .*............* *.............. *.............* **************. ............... ............... ....****....... ...******...... ..**.****...... ...**.......... :fly: A certain c/3 {tagalong} found by David Bell, April 1992. Shown here attached to the back of a small spaceship (also by Bell). ..*............................... .*.*.............................. .*.*......................*.*...*. .*.......................**.*.*..* ...........***........*.........*. **.........**..*.**...*..****..... .*.*.........****..*.*..**....**.. .**........*..*...***.....***..... ..*.......*....*..**..**..*..*.... ...*..*...*....*..***.*.*....**... .......*.**....*..****.....*...... ....**...**....*..****.....*...... ....*.*...*....*..***.*.*....**... ...**.....*....*..**..**..*..*.... ....*.*....*..*...***.....***..... .....*.......****..*.*..**....**.. ...........**..*.**...*..****..... ...........***........*.........*. .........................**.*.*..* ..........................*.*...*. :flying machine: = {Schick engine} :fore and back: (p2) Compare {snake pit}. Found by Achim Flammenkamp, July 1994. **.**.. **.*.*. ......* ***.*** *...... .*.*.** ..**.** :forward glider: A {glider} which moves at least partly in the same direction as the {puffer}(s) or {spaceship}(s) under consideration. :fountain: (p4) Found by Dean Hickerson in November 1994, and named by Bill Gosper. See also {filter}. .........*......... ................... ...**.*.....*.**... ...*.....*.....*... ....**.**.**.**.... ................... ......**...**...... **...............** *..*...*.*.*...*..* .***.*********.***. ....*....*....*.... ...**.........**... ...*...........*... .....*.......*..... ....**.......**.... :fourteener: (p1) ....**. **..*.* *.....* .*****. ...*... :fox: (p2) This is the smallest asymmetric p2 oscillator. Found by Dave Buckingham, July 1977. ....*.. ....*.. ..*..*. **..... ....*.* ..*.*.* ......* :French kiss: (p3) Found by Robert Wainwright, July 1971. *......... ***....... ...*...... ..*..**... ..*....*.. ...**..*.. ......*... .......*** .........* :frog II: (p3) Found by Dave Buckingham, October 1972. ..**...**.. ..*.*.*.*.. ....*.*.... ...*.*.*... ...**.**... .**.....**. *..*.*.*..* .*.*...*.*. **.*...*.** ....***.... ........... ...*.**.... ...**.*.... :fumarole: (p5) Found by Dean Hickerson in September 1989. In terms of its 7x8 bounding box this is the smallest p5 oscillator. ...**... .*....*. .*....*. .*....*. ..*..*.. *.*..*.* **....** :fuse: A {wick} burning at one end. For examples, see {baker}, {beacon maker}, {blinker ship}, {boat maker}, {cow}, {harvester}, {lightspeed wire}, {pi ship}, {reverse fuse}, {superstring} and {washerwoman}. Useful fuses are usually {clean}. :galaxy: = {Kok's galaxy} :Game of Life: = {Life} :Garden of Eden: A configuration of ON and OFF cells that can only occur in generation 0. (This term was first used in connection with cellular automata by John W. Tukey, many years before Life.) It was known from the start that there are Gardens of Eden in Life, because of a theorem by Edward Moore that guarantees their existence in a wide class of cellular automata. Explicit examples have since been constructed, the first by Roger Banks, et al. at MIT in 1971. This example was 9 x 33. In 1974 J. Hardouin-Duparc, et al. produced a 6 x 122 example. The following shows a 14 x 14 example (with 143 ON cells) by Achim Flammenkamp (1991 or 1992). **.*.*.*.**.*. *.***.***.**.* ****.***.**.*. ***.*.*.*.**** .***.*.***.**. *******.****.* .*.*.********. *.***.**.*.*.* ******.******. *.**.*****.*.* ***.*********. .***.*.*.*.*** ***.*.*.*.**.* *.************ :generation: The fundamental unit of time. The starting pattern is generation 0. :germ: (p3) Found by Dave Buckingham, September 1972. ....**.... .....*.... ...*...... ..*.****.. ..*....*.. .**.*..... ..*.*.**** *.*.*....* **...***.. .......**. :gfind: A program by David Eppstein used for searching for new {spaceship}s. It was with gfind that Eppstein found the {weekender}, and Paul Tooke later used it to find the {dragon}. Compare {lifesrc}. :glasses: (p2) Compare {scrubber} and {spark coil}. ....*........*.... ..***........***.. .*..............*. .*..***....***..*. **.*...*..*...*.** ...*...****...*... ...*...*..*...*... ....***....***.... .................. ....**.*..*.**.... ....*.**..**.*.... :glider: (c/4 diagonally, p4) The smallest, most common and first discovered {spaceship}. This was found by Richard Guy in 1970 while Conway's group was attempting to track the evolution of the {R-pentomino}. The name is due in part to the fact that it is {glide symmetric}. (It is often stated that Conway discovered the glider, but he himself has said it was Guy. See also the cryptic reference ("some guy") in {Winning Ways}.) *** *.. .*. The term "glider" is also occasionally (mis)used to mean "spaceship". :glider-block cycle: An infinite {oscillator} based on the following reaction (a variant of the {rephaser}). The oscillator consists of copies of this reaction displaced 2n spaces from one another (for some n>6) with blocks added between the copies in order to cause the reaction to occur again halfway through the period. The period of the resulting infinite oscillator is 8n-20. (Alternatively, in a cylindrical universe of width 2n the oscillator just consists of two gliders and two blocks.) ...**... ...**... ........ ........ ..*..*.. *.*..*.* .**..**. :glider construction: = {glider synthesis} :gliderless: A {gun} is said to be gliderless if it does not use {glider}s. The purist definition would insist that a glider does not appear anywhere, even incidentally. For a long time the only known way to construct {LWSS}, {MWSS} and {HWSS} guns involved gliders, and it was not until April 1996 that Dieter Leithner constructed the first gliderless gun (a p46 LWSS gun). The following diagram shows Leithner's p44 MWSS gun which he discovered in April 1997 (shown with Stephen Silver's May 1998 improvement to the {bounding box} using a modified {eater2}). This is the smallest known gliderless gun, and also the smallest known MWSS gun. It is based on an important p44 oscillator discovered by Dave Buckingham in early 1992. (Note that a glider shape appears in this gun for three consecutive generations, but always as part of a larger {cluster}, so even a purist would regard this gun as gliderless.) .........**....**....**........................... ........*..*.*....*.*..*.......................... ........***..........***.......................... ...........**......**............................. ..........*..******..*............................ ..........**........**............................ .................................*................ ...............................***................ ..............................*........***........ ..............................**.......*..*....... .........................*.............*.......... ........................*..............*...*...... .........................**............*.......... ........................*.*.............*.*....... .................................................. .......................*.*.....***..............** ........................*.....*..*...............* **............***.......*......**...........**.*.. **...........*...*..........................**.**. .............**.**................................ .................................**.........**.**. ..............................**.............*.*.. .............................................*.*.. ..............................................*... .............**.**.............*.*................ **...........*...*.............**................. **............***................................. ...........................**..................... ...........................*.*.................... .............................*.................... .............................**................... .................................................. .................................................. .................................................. .................................................. .................................................. .................................................. .................................................. ..........**........**............................ ..........*..******..*............................ ...........**......**............................. ........***..........***.......................... ........*..*.*....*.*..*.......................... .........**....**....**........................... :glider pusher: An arrangement of a {queen bee shuttle} and a {pentadecathlon} that can push the path of a passing glider out by one half-diagonal space. This was found by Dieter Leithner in December 1993 and is shown below. It is useful for constructing complex {gun}s where it may be necessary to produce a number of gliders travelling on close parallel paths. See also {edge shooter}. .........**.............. .........**.............. ......................... ..........*.............. .........*.*............. .........*.*............. ..........*.............. ......................... ......................... .......**.*.**........... .......*.....*........... ........*...*............ .*.......***............. ..*...................... ***...................... ......................... ......................... .................*....*.. ...............**.****.** .................*....*.. :gliders by the dozen: (stabilizes at time 184) In early references this is usually shown in a larger form whose generation 1 is generation 8 of the form shown here. **..* *...* *..** :glider synthesis: Construction of an object by means of {glider} collisions. It is generally assumed that the gliders should be arranged so that they could come from infinity - that is, gliders should not have had to pass through one another to achieve the initial arrangement. Glider syntheses for all {still life}s and known {oscillator}s with at most 14 cells were found by Dave Buckingham. Perhaps the most interesting glider syntheses are those of {spaceship}s, because these can be used to create corresponding {gun}s. Many of the c/2 spaceships that are based on {standard spaceship}s have been synthesized, mostly by Mark Niemiec. In June 1998 Stephen Silver found syntheses for some of the {Cordership}s (although it was not until July 1999 that Jason Summers built a Cordership gun). All other spaceships (except the glider itself, of course) have so far eluded synthesis. Many of them are {space dust}. A 3-glider synthesis of a {pentadecathlon} is shown in the diagram below. This was found in April 1997 by Heinrich Koenig and came as a surprise, as it was widely assumed that anything using just three gliders would already be known. ......*... ......*.*. ......**.. .......... ***....... ..*....... .*.....**. ........** .......*.. :glider train: A certain {puffer} that produces two rows of {block}s and two backward {glider} waves. Ten of these were used to make the first {breeder}. :glide symmetric: Undergoing simultaneous reflection and translation. A glide symmetric {spaceship} is commonly called a {flipper}. :gnome: = {fox} :GoE: = {Garden of Eden} :GoL: = {Game of Life} :Gosper glider gun: The first known {gun}, and indeed the first known finite pattern with unbounded growth, found by Bill Gosper in November 1970. It remains by far the smallest known gun. Gosper has since found other guns, see {new gun} and the p144 gun shown under {factory}. ........................*........... ......................*.*........... ............**......**............** ...........*...*....**............** **........*.....*...**.............. **........*...*.**....*.*........... ..........*.....*.......*........... ...........*...*.................... ............**...................... :gourmet: (p32) Found by Dave Buckingham in March 1978. Compare with {pi portraitor} and {popover}. ..........**........ ..........*......... ..*.**.**.*.....**.. ..**.*.*.*......*... ........*........*.. ................**.. .................... ................**.. *.........***..*.*.. ***.......*.*...*... ...*......*.*....*** ..*.*..............* ..**................ .................... ..**................ ..*........*........ ...*......*.*.*.**.. ..**.....*.**.**.*.. .........*.......... ........**.......... :grammar: A set of rules for connecting components together to make an object such as a {spaceship}, {oscillator} or {still life}. :grandfather: = {grandparent} :grandparent: A pattern is said to be a grandparent of the pattern it gives rise to after two generations. See also {parent}. :Gray counter: (p4) Found in 1971. If you look at this in the right way you will see that it cycles through the Gray codes from 0 to 3. Compare with {R2D2}. ......*...... .....*.*..... ....*.*.*.... .*..*...*..*. *.*.*...*.*.* .*..*...*..*. ....*.*.*.... .....*.*..... ......*...... :great on-off: (p2) ..**.... .*..*... .*.*.... **.*..*. ....**.* .......* ....***. ....*... :grey counter: = {Gray counter} (This form is erroneous, as Gray is surname, not a colour.) :grin: The following common {parent} of the {block}. This name relates to the infamous {Cheshire cat}. See also {pre-block}. *..* .**. :growing spaceship: An object that moves like a {spaceship}, except that its front part moves faster than its back part and a {wick} extends between the two. Put another way, a growing spaceship is a {puffer} whose output is burning {clean}ly at a slower rate than the puffer is producing it. Examples include {blinker ship}s and {pi ship}s. :gull: = {elevener} :gun: Any stationary pattern that emits {spaceship}s (or {rake}s) forever. For examples see {double-barrelled}, {edge shooter}, {factory}, {gliderless}, {Gosper glider gun}, {new gun} and {true}. :gunstar: Any of a series of glider {gun}s of period 144+72n (for all non-negative integers n) constructed by Dave Buckingham in 1990 based on his {transparent block reaction} and Robert Wainwright's p72 oscillator (shown under {factory}). :half bakery: See {bi-loaf}. :half fleet: = {ship-tie} :hammer: To hammer a {LWSS}, {MWSS} or {HWSS} is to smash things into the rear end of it in order to transform it into a different type of {spaceship}. A hammer is the object used to do the hammering. In the following example by Dieter Leithner a LWSS is hammered by two more LWSS to make it into a MWSS. *..*................ ....*...**.......... *...*..***.....****. .****..**.*....*...* ........***....*.... .........*......*..* :hammerhead: A certain front end for c/2 spaceships. The central part of the hammerhead pattern is supported between two {MWSS}. The picture below shows a small example of a {spaceship} with a hammerhead front end (the front 9 columns). ................*.. .**...........*...* **.***.......*..... .*****.......*....* ..*****.....*.****. ......***.*.**..... ......***....*..... ......***.***...... ..........**....... ..........**....... ......***.***...... ......***....*..... ......***.*.**..... ..*****.....*.****. .*****.......*....* **.***.......*..... .**...........*...* ................*.. :handshake: An old MIT name for {lumps of muck}, from the following form (2 generations on from the {stairstep hexomino}): ..**. .*.** **.*. .**.. :harbor: (p5) Found by Dave Buckingham in September 1978. The name is by Dean Hickerson. .....**...**..... .....*.*.*.*..... ......*...*...... ................. .....**...**..... **..*.*...*.*..** *.*.**.....**.*.* .*.............*. ................. .*.............*. *.*.**.....**.*.* **..*.*...*.*..** .....**...**..... ................. ......*...*...... .....*.*.*.*..... .....**...**..... :harvester: (c p4 fuse) Found by David Poyner, this was the first published example of a {fuse}. The name refers to the fact the it produces debris in the form of {block}s which contain the same number of cells as the fuse has burnt up. ................** ...............*.* ..............*... .............*.... ............*..... ...........*...... ..........*....... .........*........ ........*......... .......*.......... ......*........... .....*............ *****............. ****.............. *.**.............. :HashLife: A very fast Life algorithm by Bill Gosper that is designed to take advantage of the considerable amount of repetitive behaviour in many large patterns of interest. This algorithm is described by Gosper in his paper listed in the bibliography at the end of this lexicon. Roughly speaking, the basic idea is to store subpatterns in a hash table so that the results of their evolution don't have to be recomputed if they arise again somewhen, or somewhere, else. Although HashLife stores individual patterns in an economical manner, the fact that it retains earlier generations means that it can require a lot of memory. There is also the problem that it works asynchronously - at any given moment it will usually have evolved different parts of the pattern through different numbers of generations - so it is not suitable for showing a continuous display of the evolution of a pattern. :hassle: See {hassler}. :hassler: An {oscillator} that works by hassling (repeatedly moving or changing) some object. For some examples, see {Jolson}, {baker's dozen}, {toad-flipper}, {toad-sucker} and {traffic circle}. :hat: (p1) Found in 1971. See also {twinhat} and {sesquihat}. ..*.. .*.*. .*.*. **.** :heat: For an {oscillator} or {spaceship}, the average number of cells which change state in each generation. For example, the heat of a {glider} is 4, because 2 cells are born and 2 die every generation. For a period n oscillator with an r-cell {rotor} the heat is at least 2r/n and no more than r(1-(n mod 2)/n). For n=2 and n=3 these bounds are equal. :heavyweight emulator: = {HW emulator} :heavyweight spaceship: = {HWSS} :heavyweight volcano: = {HW volcano} :hebdarole: (p7) Found by Noam Elkies, November 1997. Compare {fumarole}. The smaller version shown below was found soon after by Alan Hensel using a component found by Dave Buckingham in June 1977. The top tens rows can be stabilized by their mirror image (giving an {inductor}) and this was the original form found by Elkies. ...........**........... ....**...*....*...**.... .*..*..*.*....*.*..*..*. *.*.*.**.*....*.**.*.*.* .*..*..*.*.**.*.*..*..*. ....**....*..*....**.... ...........**........... .......*..*..*..*....... ......*.**....**.*...... .......*........*....... ........................ ...**..............**... ...*..****....****..*... ....*.*.*.*..*.*.*.*.... ...**.*...****...*.**... .......**......**....... .........**..**......... .........*..*.*......... ..........**............ :hectic: (p30) Found by Robert Wainwright in September 1984. ......................**............... ......................**............... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... .........*..........**...**............ .......*.*............***.............. ......*.*............*...*............. **...*..*.............*.*.............. **....*.*..............*............... .......*.*......*.*.................... .........*......**..................... .................*...*................. .....................**......*......... ....................*.*......*.*....... ...............*..............*.*....** ..............*.*.............*..*...** .............*...*............*.*...... ..............***............*.*....... ............**...**..........*......... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ....................................... ...............**...................... ...............**...................... :Heisenburp device: A pattern which can detect the passage of a {glider} without affecting the glider's path or timing. The first such device was constructed by David Bell in December 1992. The term is due to Bill Gosper. The following is an example of the kind of reaction used at the heart of a Heisenburp device. The glider at bottom right alters the reaction of the other two gliders without itself being affected in any way. *.....*.... .**...*.*.. **....**... ........... ........... ........... .........** ........*.* ..........* :heptaplet: Any 7-cell {polyplet}. :heptapole: (p2) The {barberpole} of length 7. **........ *.*....... .......... ..*.*..... .......... ....*.*... .......... ......*.*. .........* ........** :heptomino: Any 7-cell {polyomino}. There are 108 such objects. Those with names in common use are the {B-heptomino}, the {Herschel} and the {pi-heptomino}. :Herschel: (stabilizes at time 128) The following pattern which occurs at generation 20 of the {B-heptomino}. *.. *** *.* ..* :Herschel conduit: A {conduit} that moves a {Herschel} from one place to another. See also {Herschel loop}. Sixteen simple {stable} Herschel conduits are currently known, having been discovered from 1995 onwards by Dave Buckingham (DJB) and Paul Callahan (PBC). These are shown in the following table. In this table "steps" is the number of {step}s, "m" tells how the Herschel is moved (R = turned right, L = turned left, B = turned back, F = unturned, f = flipped), and "dx" and "dy" give the displacement of the centre cell of the Herschel (assumed to start in the orientation shown above). ------------------------------------ steps m dx dy discovery ------------------------------------ 64 R -11 9 DJB, Sep 1995 77 Ff -25 -8 DJB, Aug 1996 112 L -12 -33 DJB, Jul 1996 116 F -32 1 PBC, Feb 1997 117 F -40 -6 DJB, Jul 1996 119 Ff -20 14 DJB, Sep 1996 125 Bf 9 -17 PBC, Nov 1998 153 Ff -48 -4 PBC, Feb 1997 156 L -17 -41 DJB, Aug 1996 158 Ff -27 -5 DJB, Jul 1996 166 F -49 3 PBC, May 1997 176 Ff -45 0 PBC, Oct 1997 190 R -24 16 DJB, Jul 1996 200 Lf -17 -40 PBC, Jun 1997 202 Rf -7 32 DJB, May 1997 222 Bf 6 -16 PBC, Oct 1998 ------------------------------------ :Herschel loop: A cyclic {Herschel track}. Although no loop of length less than 256 generations has been constructed it is possible to make {oscillator}s of smaller periods by putting more than one Herschel in the track. In this way oscillators, and in most cases {gun}s, of all periods from 54 onwards can now be constructed (although the p55 case is a bit strange, shooting itself with gliders in order to stabilize itself). See also {emu} and {omniperiodic}. :Herschel track: A {track} for {Herschel}s. See also {B track}. :Hertz oscillator: (p8) Compare {negentropy}, and also {cauldron}. Found by Conway's group in 1970. ...**.*.... ...*.**.... ........... ....***.... ...*.*.*.** ...*...*.** **.*...*... **.*...*... ....***.... ........... ....**.*... ....*.**... :hexadecimal: = {beehive and dock} :hexaplet: Any 6-cell {polyplet}. :hexapole: (p2) The {barberpole} of length 6. **....... *.*...... ......... ..*.*.... ......... ....*.*.. ......... ......*.* .......** :hexomino: Any 6-cell {polyomino}. There are 35 such objects. For some examples see {century}, {stairstep hexomino}, {table}, {toad} and {Z-hexomino}. :H-heptomino: Name given by Conway to the following {heptomino}. After one generation this is the same as the {I-heptomino}. **.. .*.. .*** ..*. :hive: = {beehive} :hivenudger: (c/2 orthogonally, p4) A {spaceship} found by Hartmut Holzwart in July 1992. (The name is due to Bill Gosper.) It consists of a {pre-beehive} escorted by four {LWSS}. In fact any LWSS can be replaced by a {MWSS} or a {HWSS}, so that there are 45 different single-hive hivenudgers. ****.....*..* *...*...*.... *.......*...* .*..*...****. ............. .....**...... .....**...... .....**...... ............. .*..*...****. *.......*...* *...*...*.... ****.....*..* :honeycomb: (p1) ..**.. .*..*. *.**.* .*..*. ..**.. :honey farm: (p1) A common formation of four beehives. ......*...... .....*.*..... .....*.*..... ......*...... ............. .**.......**. *..*.....*..* .**.......**. ............. ......*...... .....*.*..... .....*.*..... ......*...... :hook: Another term for a {bookend}. It is also used for other hook-shaped things, such as occur in the {eater1} and the {hook with tail}, for example. :hook with tail: (p1) For a long time this was the smallest {still life} without a well-established name. It is now a vital component of the smallest known {HWSS} {gun}, where it acts as a {rock}. *.*.. **.*. ...*. ...** :houndstooth agar: The p2 {agar} that results from tiling the plane with the following pattern. .*** .*.. ..*. ***. :house: The following {induction coil}. It is generation 3 of the {pi-heptomino}. See {spark coil} and {dead spark coil}. .***. *...* **.** :hustler: (p3) Found by Robert Wainwright, June 1971. .....**.... .....**.... ........... ...****.... *.*....*... **.*...*... ...*...*.** ...*....*.* ....****... ........... ....**..... ....**..... :hustler II: (p4) ....*........... ....***......... .......*........ ......*..**..... *.**.*.**..*.... **.*.*.....*.... .....*....*..... ....*.....*.*.** ....*..**.*.**.* .....**..*...... ........*....... .........***.... ...........*.... :HW emulator: (p4) Found by Robert Wainwright in June 1980. See also {emulator}. .......**....... ..**.*....*.**.. ..*..........*.. ...**......**... ***..******..*** *..*........*..* .**..........**. :HWSS: (c/2 orthogonally, p4) The fourth most common {spaceship}. Found by Conway in 1970. ...**.. .*....* *...... *.....* ******. :HWSS emulator: = {HW emulator} :HW volcano: (p5) A p5 {domino} {sparker}, found by Dean Hickerson in February 1995. There are at least two known forms for this, one of which is shown below. .........*.......................... ........*.*......................... ......***.*......................... .....*....**.*...................... .....*.**...**......**.............. ....**.*.**.........*.*............. .........*.*****......*..*.**....... ..*.**.**.*.....*....**.*.**.*...... .....**.....****........*....*...... *...*.*..*...*.*....**.*.****.**.... *...*.*..**.*.**.**....*.*....*.*... .....**...***.**.*.***.*..***...*... ..*.**.**.**.............*.*..*.*.** ...........*......*.*.*.*..**.*.*.*. ....**.*.*.**......**.*.*.*...*.*.*. .....*.**.*..*.......*.**..****.**.. .....*....*.*........*...**......... ....**....**........**...*..*....... ...........................**....... :I-heptomino: Name given by Conway to the following {heptomino}. After one generation this is the same as the {H-heptomino}. **.. .*.. .**. ..** :IMG: = {intermitting glider gun} :Immigration: A form of {colorized Life} in which there are two types of ON cell, a newly-born cell taking the type of the majority of its three {parent cells} and surviving cells remaining of the same type as in the previous generation. :induction coil: Any object used to stabilize an edge (or edges) without touching. The tubs used in the {Gray counter} are examples, as are the blocks and snakes used in the {Hertz oscillator} and the heptomino at the bottom of the {mathematician}. :inductor: Any {oscillator} with a row of dead cells down the middle and whose two halves are mirror images of one another, both halves being required for the oscillator to work. The classic examples are the {pulsar} and the {tumbler}. If still lifes are considered as p1 oscillators then there are numerous simple examples such as {table on table}, {dead spark coil} and {cis-mirrored R-bee}. Some spaceships, such as the {brain}, the {snail} and the {spider} use the same principle. :infinite growth: Growth of a finite pattern such that the {population} tends to infinity, or at least is unbounded. The first known pattern with infinite growth was the {Gosper glider gun}. An interesting question is: What is the minimum population of a pattern that exhibits infinite growth? In 1971 Charles Corderman found that a {switch engine} could be stabilized by a {pre-block} in a number of different ways, giving 11-cell patterns with infinite growth. This record stood for more than quarter of a century until Paul Callahan found, in November 1997, two 10-cell patterns with infinite growth. The following month he found the one shown below, which is much neater, being a single {cluster}. This produces a stabilized switch engine of the block-laying type. ......*. ....*.** ....*.*. ....*... ..*..... *.*..... Nick Gotts and Paul Callahan have also shown that there is no infinite growth pattern with fewer than 10 cells, so that the question has now been answered. Also of interest is the following pattern (again found by Callahan), which is the only 5x5 pattern with infinite growth. This too emits a block-laying switch engine. ***.* *.... ...** .**.* *.*.* Following a conjecture of Nick Gotts, Stephen Silver produced, in May 1998, a pattern of width 1 which exhibits infinite growth. This pattern was very large (12470x1 in the first version, reduced to 5447x1 the following day). In October 1998 Paul Callahan did an exhaustive search, finding the smallest example, the 39x1 pattern shown below. This produces two block-laying switch engines, stability being achieved at generation 1483. ********.*****...***......*******.***** Although the simplest infinite growth patterns grow at a rate that is (asymptotically) linear, many other types of growth rate are possible, quadratic growth (see {breeder}) being the fastest. Dean Hickerson has found many patterns with unusual growth rates, such as {sawtooth}s and a {caber tosser}. See also {Fermat prime calculator}. :initials: = {monogram} :integral: = {integral sign} :integral sign: (p1) ...** ..*.* ..*.. *.*.. **... :intentionless: = {elevener} :interchange: (p2) A common formation of six blinkers. ..***....***.. .............. *............* *............* *............* .............. ..***....***.. :intermitting glider gun: Despite the name, an intermitting glider gun (IMG) is more often an {oscillator} than a {gun}. There are two basic types. A type 1 IMG consists of two guns firing at one another in such a way that each gun is temporarily disabled on being hit by a glider from the other gun. A type 2 IMG consists of a single gun firing at a 180-degree glider {reflector} in such a way that returning gliders temporarily disable the gun. Both types of IMG can be used to make glider guns of periods that are multiples of the base period. This is done by firing another gun across the two-way intermittent glider stream of the IMG in such a way that gliders only occasionally escape. :island: The unconnected {polyplet}s of which a {stable} pattern consists are sometimes called islands. So, for example, a {boat} has only one island, while an {aircraft carrier} has two, a {honey farm} has four and the standard form of the {eater3} has five. :J: = {Herschel} :jack: (p4) Found by Robert Wainwright, April 1984. ...*.....*... ...**...**... *..**...**..* ***..*.*..*** .....*.*..... ***..*.*..*** *..**...**..* ...**...**... ...*.....*... :jam: (p3) Found by Achim Flammenkamp in 1988, but not widely known about until rediscovered (and named) by Dean Hickerson in September 1989. Compare with {mold}. In fact this is really very like {caterer}. In terms of its 7x7 {bounding box} it ties with {trice tongs} as the smallest p3 {oscillator}. ...**. ..*..* *..*.* *...*. *..... ...*.. .**... :Jaws: A {breeder} constructed by Nick Gotts in February 1997. In the original version Jaws had an initial {population} of 150, which at the time was the smallest for any known pattern with superlinear growth. In November 1997 Gotts produced a 130-cell Jaws using some {switch engine} {predecessor}s found by Paul Callahan. Jaws has since been beaten by the even smaller {mosquito}s, {teeth} and {catacryst}. Jaws consists of eight pairs of switch engines which produce a new block-laying switch engine (plus masses of junk) every 10752 generations. It is therefore an MMS breeder. :JC: = {dead spark coil} :JHC: John Horton Conway. Also another name for {monogram}. :J-heptomino: = {Herschel} :Jolson: (p15) Two {block}s {hassle}d by two {pentadecathlon}s. Found by Robert Wainwright in November 1984 and named by Bill Gosper. A p9 version using {snacker}s instead of pentadecathlons is also possible. .**......**.. *..*....*..*. *..*....*..*. *..*....*..*. .**......**.. ............. ............. .......*..... .....*..*.**. ......**..**. ............. ............. ......****... .....******.. ....********. ...**......** ....********. .....******.. ......****... :keys: See {short keys}, {bent keys} and {odd keys}. :kickback reaction: The following collision of two {glider}s whose product is a single glider travelling in the opposite direction to one of the original gliders. This is important in the proof of the existence of a {universal constructor}, and in Bill Gosper's {total aperiodic}, as well as a number of other constructions. .....*.. ......** .**..**. *.*..... ..*..... :kidney: A Gosperism for {century}. See also {diuresis}. :killer toads: A pair of {toad}s acting together so that they can eat things. Here, for example, are some killer toads eating a {HWSS}. Similarly they can eat a {MWSS} (but not a {LWSS}). For another example see {twirling T-tetsons II}. See also {candlefrobra}. ..**.......*** *....*....***. ......*....... *.....*....... .******....... ..........***. ...........*** :knightship: Any {spaceship} of type (2m,m)/n. Such spaceships do exist (see {universal constructor}), but no concrete example is known. A knightship must be asymmetric and its period must be at least 6, which makes searching for them using programs like {lifesrc} very difficult. By analogy with the corresponding fairy chess pieces, spaceships of types (3m,m)/n, (3m,2m)/n and (4m,m)/n would presumably be called camelships, zebraships and giraffeships, respectively. But no examples of these are known either, and they are even more difficult to search for. :Kok's galaxy: (p8) Found by Jan Kok in 1971. See {converter} for a use of this {sparker}. ******.** ******.** .......** **.....** **.....** **.....** **....... **.****** **.****** :lake: Any still life consisting of a simple closed curve made from diagonally connected {domino}es. The smallest example is the {pond}, and the next smallest is this (to which the term is sometimes restricted): ....**.... ...*..*... ...*..*... .**....**. *........* *........* .**....**. ...*..*... ...*..*... ....**.... :Laputa: (p2) Found by Rich Schroeppel, September 1992. ...**.**.... ...**.*...** ........*..* .******.***. *..*.*...... **...*.**... ....**.**... :large S: = {big S} :Life: A 2-dimensional 2-state {cellular automaton} discovered by John Conway in 1970. The states are referred to as ON and OFF (or live and dead). The transistion rule is as follows: a cell that is ON will remain ON in the next generation if and only if exactly 2 or 3 of the 8 adjacent cells are also ON, and a cell that is OFF will turn ON if and only if exactly 3 of the 8 adjacent cells are ON. (This is more succinctly stated as: "If 2 of your 8 nearest neighbours are ON, don't change. If 3 are ON, turn ON. Otherwise, turn OFF.") :Life32: A freeware Life program by Johan Bontes for Microsoft Windows 95/98/NT. :LifeLine: A newletter edited by Robert Wainwright from 1971 to 1973. During this period it was the main forum for discussions about Life. The newletter was nominally quarterly, but the actual dates of its eleven issues were as follows: Mar, Jun, Sep, Dec 1971 Sep, Oct, Nov, Dec 1972 Mar, Jun, Sep 1973 :Lifenthusiast: A Life enthusiast. Term coined by Robert Wainwright. :lifesrc: David Bell's Life search program, for finding new {spaceship}s and {oscillator}s. This is a C implementation of an algorithm developed by Dean Hickerson in 6502 assembler. Most of the spaceships and many of the oscillators shown in this lexicon were found with lifesrc or by Hickerson's original program. The lifesrc algorithm is only useful for very small periods, as the amount of computing power required rises rapidly with increaing period. Compare {gfind}. :light bulb: (p2) Found in 1971. .**.*.. .*.**.. ....... ..***.. .*...*. .*...*. ..*.*.. *.*.*.* **...** The same {rotor} can be embedded in a slightly smaller {stator} like this: ...*..... .***..... *........ ******... ......*.. ..*...*.. ..**.*... ......*** ........* :lightspeed ribbon: = {superstring} :lightspeed wire: Any {wick} that can burn non-destructively at the speed of light. These are potentially useful for various things, but so far no-one has found the necessary mechanisms. The following diagram shows an example of a lightspeed wire, with a small defect that travels along it at the speed of light. ....**..**..**..**..**..**..**..**..**..**..**..**..**.... ....**..**..**..**..**..**..**..**..**..**..**..**..**.... .......................................................... ..******************************************************.. .*......*...............................................*. *.*****....*********************************************.* .*.....*................................................*. ..******************************************************.. .......................................................... ....**..**..**..**..**..**..**..**..**..**..**..**..**.... ....**..**..**..**..**..**..**..**..**..**..**..**..**.... :lightweight emulator: = {LW emulator} :lightweight spaceship: = {LWSS} :lightweight volcano: = {toaster} :line puffer: A {puffer} which produces its output by means of an orthogonal line of cells at right angles to the direction of travel. The archetypal line puffer was found by Alan Hensel in March 1994, based on a {spaceship} found earlier that month by Hartmut Holzwart. The following month Holzwart found a way to make extensible c/2 line puffers, and Hensel found a much smaller stabilization the following day. But in October 1995 Tim Coe discovered that for large widths these were often unstable, although typically lasting millions of generations. In May 1996, however, Coe found a way to fix the instability. The resulting puffers appear to be completely stable and to exhibit an exponential increase in period as a function of width, although neither of these things has been proved. Line puffers have enabled the construction of various difficult periods for c/2 spaceships and puffers, including occasionally periods which are not multiples of 4 and which would therefore be impossible to attain with the usual type of construction based on {standard spaceship}s. In particular, the first c/2 {rake} with period not divisible by 4 was achieved in January 2000 when David Bell constructed a p42 {backrake} by means of line puffers. See also {puff suppressor}. :loading dock: (p3) Found by Dave Buckingham, September 1972. ....*.... ..***.... .*...**.. *.**...*. .*...**.* ..**...*. ....***.. ....*.... :loaf: (p1) .**. *..* .*.* ..*. :loaflipflop: (p15) Here four {pentadecathlon}s {hassle} a {loaf}. Found by Robert Wainwright in 1990. ................*................. ...............***................ .................................. .................................. ...............***................ .................................. ...............*.*................ ...............*.*................ .................................. ...............***................ .................................. .................................. ...............***................ ................*................. .................................. .*..*.**.*..*...............**.... **..*....*..**...**.......*....*.. .*..*.**.*..*...*..*.....*......*. ................*.*.....*........* .................*......*........* ........................*........* .........................*......*. ..........................*....*.. ............................**.... ..................***............. .................*...*............ ................*.....*........... .................................. ...............*.......*.......... ...............*.......*.......... .................................. ................*.....*........... .................*...*............ ..................***............. :loaf on loaf: = {bi-loaf} :loaf siamese barge: (p1) ..**. .*..* *.*.* .*.*. ..*.. :LoM: = {lumps of muck} :lone dot agar: An {agar} in which every live cell is isolated in every generation. :lonely bee: = {worker bee} :long: A term applied to an object that is of the same basic form as some standard object, but longer. For examples see {long barge}, {long boat}, {long bookend}, {long canoe}, {long shillelagh}, {long ship} and {long snake}. :long^3: The next degree of longness after {long long}. Some people prefer "extra long". :long^4: The next degree of longness after {long^3}. Some people prefer "extra extra long". :long barge: (p1) .*... *.*.. .*.*. ..*.* ...*. :long boat: (p1) .*.. *.*. .*.* ..** :long bookend: The following {induction coil}. ...** *...* ****. :long canoe: (p1) ....** .....* ....*. ...*.. *.*... **.... :long hat: = {loop} :long hook: = {long bookend} :long house: = {dock} :long integral: (p1) ..** .*.* .*.. ..*. *.*. **.. :long long: The next degree of longness after {long}. Some people prefer "very long". :long long barge: (p1) .*.... *.*... .*.*.. ..*.*. ...*.* ....*. :long long boat: (p1) .*... *.*.. .*.*. ..*.* ...** :long long canoe: (p1) .....** ......* .....*. ....*.. ...*... *.*.... **..... :long long ship: (p1) **... *.*.. .*.*. ..*.* ...** :long long snake: (p1) **.... *.*... ...*.* ....** :long shillelagh: (p1) **..** *..*.* .**... :long ship: (p1) **.. *.*. .*.* ..** :long sinking ship: = {long canoe} :long snake: (p1) **... *.*.* ...** :loop: (p1) .**.. *..*. .*.*. **.** :low-denisty Life: = {sparse Life} :lumps of muck: The common evolutionary sequence that ends in the {blockade}. The name is sometimes used of the blockade itself, and can in general be used of any stage of the evolution of the {stairstep hexomino}. :LW emulator: (p4) The smallest {emulator}, found by Robert Wainwright in June 1980. ..**.*..*.**.. ..*........*.. ...**....**... ***..****..*** *..*......*..* .**........**. :LWSS: (c/2 orthogonally, p4) The known smallest orthogonally moving {spaceship}, and the second most common (after the {glider}). Found by Conway in 1970. .*..* *.... *...* **** :LWSS emulator: = {LW emulator} :LW volcano: = {toaster} :mango: (p1) .**.. *..*. .*..* ..**. :mathematician: (p5) Found by Dave Buckingham, 1972. ....*.... ...*.*... ...*.*... ..**.**.. *.......* ***...*** ......... ********* *.......* ...****.. ...*..**. :Max: A name for the smallest known {spacefiller}. The name represents the fact that the growth rate is the fastest possible. (This has not quite been proved, however. There remains the possibility, albeit not very likely, that a periodic {agar} could have an average {density} greater than 1/2, and a spacesfiller stretching such an agar at the same speed as the known spacefillers would have a faster average growth rate.) :mazing: (p4) In terms of its minimum {population} of 12 this ties with {mold} as the smallest p4 {oscillator}. Found by Dave Buckingham in December 1973. ...**.. .*.*... *.....* .*...** ....... ...*.*. ....*.. :medium fish: = {MWSS} :metamorphosis: An {oscillator} built by Robert Wainwright that uses the following reaction (found by Bill Gosper) to turn {glider}s into {LWSS}, and converts these LWSS back into gliders by colliding them head on. (There are in fact two ways to do the following reaction, because the {spark} of the {twin bees shuttle} is symmetric.) ...................*......... ....................*........ ..................***........ ............................. ............................. ............................. ............................. ............................. ............*...*.....*.**... **.........*.....*....*.*.*.. **.........*.........*....*.. ...........**...*.....*.*.*.. .............***......*.**... ............................. .............***............. ...........**...*............ **.........*...............** **.........*.....*.........** ............*...*............ :metamorphosis II: An oscillator built by Robert Wainwright in December 1994 based on the following p30 {glider}-to-{LWSS} {converter}. This converter was first found by Paul Rendell, January 1986 or earlier, but wasn't widely known about until Paul Callahan rediscovered it in December 1994. ......................*. .....................*.. .....................*** ........................ ........................ .........*.*............ .........*..*........... **..........**.......... **........*...**........ .....**.....**.......... ....*....*..*........... .........*.*............ ........................ ........................ ........................ ........................ ................*....... ...............***...... ..............*****..... .............*.*.*.*.... .............**...**.... ........................ ........................ ................*....... ...............*.*...... ...............*.*...... ................*....... ...............**....... ...............**....... ...............**....... :methuselah: Any small pattern that stabilizes only after a long time. Term coined by Conway. Examples include the {R-pentomino}, {acorn} and {bunnies}. :middleweight emulator: = {MW emulator} :middleweight spaceship: = {MWSS} :middleweight volcano: = {MW volcano} :mini pressure cooker: (p3) Found by Robert Wainwright before June 1972. Compare {pressure cooker}. .....*..... ....*.*.... ....*.*.... ...**.**... *.*.....*.* **.*.*.*.** ...*...*... ...*.*.*... ....*.*.... .....*..... :M.I.P. value: The maximum {population} divided by the initial population for an unstable pattern. For example, the {R-pentomino} has an M.I.P. value of 63.8, since its maximum population is 319. The term is no longer in use. :MIT oscillator: = {cuphook} :MMM breeder: See {breeder}. :MMS breeder: See {breeder}. :mod: The smallest number of generations it takes for an {oscillator} or {spaceship} to reappear in its original form, possibily subject to some rotation or reflection. The mod may be equal to the {period}, but it may also be a quarter of the period (for oscillators that rotate 90 degrees every quarter period) or half the period (for other oscillators which rotate 180 degrees every half period, and also for {flipper}s). :mold: (p4) Found by Achim Flammenkamp in 1988, but not widely known until Dean Hickerson rediscovered it (and named it) in August 1989. Compare with {jam}. In terms of its minimum {population} of 12 it ties with {mazing} as the smallest p4 {oscillator}. But in terms of its 6x6 {bounding box} it wins outright. In fact, of all oscillators that fit in a 6x7 box it is the only one with {period} greater than 2. ...**. ..*..* *..*.* ....*. *.**.. .*.... :monogram: (p4) Found by Dean Hickerson, August 1989. **...** .*.*.*. .**.**. .*.*.*. **...** :moose antlers: (p1) **.....** *.......* .***.***. ...*.*... ....*.... :mosquito: See {mosquito1}, {mosquito2}. {mosquito3}, {mosquito4} and {mosquito5}. :mosquito1: A {breeder} constructed by Nick Gotts in September 1998. The original version had an initial population of 103, which was then the smallest for any known pattern with superlinear growth (beating the record previously held by {Jaws}). This was reduced to 97 by Stephen Silver the following month, but was then almost immediately superceded by {mosquito2}. Mosquito1 consists of the classic {puffer train} plus four {LWSS} and four {MWSS} (mostly in {predecessor} form, to keep the population down). Once it gets going it produces a new block-laying {switch engine} (plus a lot of junk) every 280 generations. It is therefore an MMS breeder, albeit a messy one. :mosquito2: A {breeder} constructed by Nick Gotts in October 1998. Its initial population of 85 was for a couple of hours the smallest for any known pattern with superlinear growth, but was then beaten by {mosquito3}. Mosquito2 is very like {mosquito1}, but uses two fewer {MWSS} and one more {LWSS}. :mosquito3: A {breeder} constructed by Nick Gotts in October 1998. Its initial population of 75 was at the time the smallest for any known pattern with superlinear growth, but was beaten a few days later by {mosquito4}. Mosquito3 has one less {LWSS} than {mosquito2}. It is somewhat different from the earlier mosquitos in that the {switch engine}s it makes are glider-producing rather than block-laying. :mosquito4: A slightly improved version of {mosquito3} which Stephen Silver produced in October 1998 making use of another discovery of Nick Gotts (September 1997): an 8-cell pattern that evolves into a {LWSS} plus some junk. Mosquito4 is a {breeder} with an initial population of 73, at the time the smallest for any known pattern with superlinear growth, but superceded a few days later by {mosquito5}. :mosquito5: A slightly improved version of {mosquito4} which Nick Gotts produced in October 1998. The improvement is of a similar nature to the improvement of mosquito4 over mosquito3. Mosquito5 is a {breeder} with an initial population of 71. At the time, this was the smallest population for any known pattern with superlinear growth, but it has since been superceded by {teeth} and {catacryst}. :mould: = {mold} :MSM breeder: See {breeder}. :multi-state Life: = {colorized Life} :multum in parvo: (stabilizes at time 3933) A {methuselah} found by Charles Corderman, but not as long-lasting as his {acorn}. ...*** ..*..* .*.... *..... :muttering moat: Any {oscillator} whose {rotor} consists of a closed chain of cells each of which is adjacent to exactly two other rotor cells. Compare {babbling brook}. Examples include the {bipole}, the {blinker}, the {clock}, the {cuphook}, the {Gray counter}, the {quad}, the {scrubber}, the {skewed quad} and the p2 {snake pit}. The following diagram shows a p2 example (by Dean Hickerson, May 1993) with a larger rotor. See {ring of fire} for a very large one. **..... *.*.**. .....*. .*..*.. ..*.... ..*.*.* .....** :MW emulator: (p4) Found by Robert Wainwright in June 1980. See also {emulator} and {filter}. .......*....... ..**.*...*.**.. ..*.........*.. ...**.....**... ***..*****..*** *..*.......*..* .**.........**. :MWSS: (c/2 orthogonally, p4) The third most common {spaceship}. Found by Conway in 1970. ...*.. .*...* *..... *....* *****. :MWSS emulator: = {MW emulator} :MWSS out of the blue: The following reaction, found by Peter Rott in November 1997, in which a {LWSS} passing by a p46 {oscillator} creates a {MWSS} travelling in the opposite direction. Together with some reactions found by Dieter Leithner, and a LWSS-turning reaction which Rott had found in November 1993 (but which was not widely known until Paul Callahan rediscovered it in June 1994) this can be used to prove that there exist {gliderless} guns for LWSS, MWSS and {HWSS} for every period that is a multiple of 46. *..*................................. ....*................................ *...*................................ .****................................ ..................................... ..................................... ..................................... ..................................... ..................................... ...................**..............** ..................**...............** ...................*****............. ..**................****............. ..**.....*........................... ........***.........****............. .......*.*.*.......*****............. ........*..*......**...............** ........***........**..............** .........*........................... ..................................... ..................................... ..................................... ..................................... ..*.......*.......................... ..................................... ***.......***........................ .**.**.**.**......................... ..***...***.......................... ...*.....*........................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..**.....**.......................... ..**.....**.......................... :MW volcano: (p5) Found by Dean Hickerson in April 1992. ......*...... ....*...*.... ............. ...*.....*... .***.***.***. *...**.**...* *.***.*.****. .*........... ...*.*.*.**.* ..**.***.*.** ...*.*..*.... ...*..**..... ..**......... :My Experience with B-heptominos in Oscillators: An article by Dave Buckingham (October 1996) that describes his discovery of {Herschel conduit}s, including sufficient (indeed ample) {stable} conduits to enable, for the first time, the construction of period n oscillators - and true period n guns - for every sufficiently large integer n. (See {Herschel loop} and {emu}.) :natural: Occurring often in random patterns. There is no precise measure of naturalness, since the most useful definition of "random" in this context is open to debate. Nonetheless, it is clear that objects such as {block}s, {blinker}s, {beehive}s and {glider}s are very natural, while {eater2}s, {dart}s, {gun}s, etc., are not. :negentropy: (p2) Compare {Hertz oscillator}. ...**.*.... ...*.**.... ........... ....***.... ...*.*.*.** ...**..*.** **.*...*... **.*...*... ....***.... ........... ....**.*... ....*.**... :neighbour: Any of the eight cells adjacent to a given cell. A cell is therefore not considered to be a neighbour of itself, although the neighbourhood used in Life does in fact include this cell (see {cellular automaton}). :new five: (p3) Found by Dean Hickerson, January 1990. ..**..... .*..*.... .*.*..*.. **.*.**.. *........ .***.**** .....*..* *.**..... **.**.... :new gun: An old name for the second known basic {gun} (found, like the first, by Bill Gosper), shown below. A number of other ways of constructing a gun from two {twin bees shuttle}s have since been found - see {edge shooter} for one of these. .........................**.....** .........................**.....** .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. ...........................**.**.. ..........................*.....*. ..............