Editing Life-like cellular automaton (section)

== A selection of {{Not a typo|Life-like}} rules ==
[[File:Diamonds.png|thumb|Chaotic diamonds in the Diamoeba (B35678/S5678) rule]]
[[File:Seeds.png|thumb|Exploding chaos in the Seeds (B2/S) rule]]
[[File:Conway.png|thumb|Conway's Game of Life (B3/S23)]]
[[File:Anneal CA.png|thumb|200px|Anneal (B4678/S35678)]]
There are 2<sup>18</sup>&nbsp;=&nbsp;262,144 possible {{Not a typo|Life-like}} rules, only a small fraction of which have been studied in any detail.
In the descriptions below, all rules are specified in Golly/RLE format.

<!-- Please do not add rules to this list unless they can be documented by at least two independent sources. -->
{| class="wikitable"
|+ Notable {{Not a typo|Life-like}} rules
! Rule !! Name !! Description and sources
|-
| B1357/S1357
| Replicator
| [[Edward Fredkin]]'s replicating automaton: every pattern is eventually replaced by multiple copies of itself.<ref name="mirekw"/><ref name="wuensche"/><ref name="e10"/>
|-
| B2/S
| [[Seeds (cellular automaton)|Seeds]]
| All patterns are phoenixes, meaning that every live cell immediately dies, and many patterns lead to explosive chaotic growth. However, some engineered patterns with complex behavior are known.<ref name="mirekw"/><ref>{{citation
 | last = Silverman | first = Brian
 | contribution = Changing the Rules
 | publisher = Mathematical Association of America
 | title = The Virtual Computer
 | url = http://www.maa.org/editorial/mathgames/seeds.html}}.</ref><ref>[http://entropymine.com/jason/life/alt/b2s.zip Patterns for Seeds] collected by Jason Summers.</ref>
|-
| B25/S4
|
| This rule supports a small self-replicating pattern which, when combined with a small glider pattern, causes the glider to bounce back and forth in a pseudorandom walk.<ref name="e10"/><ref>{{citation|first=Gabriel|last=Nivasch|title=The photon/XOR system|year=2007|url=http://www.gabrielnivasch.org/fun/life/photonxor-system}}.</ref>
|-
| B3/S012345678
| [[Life without Death|Life&nbsp;without&nbsp;Death]]
| Also known as Inkspot or Flakes. Cells that become alive never die. It combines chaotic growth with more structured ladder-like patterns that can be used to simulate arbitrary Boolean circuits.<ref name="mirekw"/><ref name="e10"/><ref>{{citation|title=Cellular Automata Machines: A New Environment for Modeling|first1=Tommaso|last1=Toffoli|author1-link=Tommaso Toffoli|first2=Norman|last2=Margolus|author2-link=Norman Margolus|year=1987|publisher=MIT Press|contribution=1.2 Animate-by-numbers|pages=6–7}}.</ref><ref>{{citation|title=Life without Death is P-complete|url=http://psoup.math.wisc.edu/java/lwodpc/lwodpc.html|journal=Complex Systems|volume=10|year=1996|pages=437–447|first1=David|last1=Griffeath|first2=Cristopher|last2=Moore|author2-link=Cris Moore}}.</ref>
|-
| B3/S23
| [[Conway's Game of Life|Life]]
| Highly complex behavior.<ref>{{citation
 | last = Gardner | first = Martin | author-link = Martin Gardner
 | date = October 1970
 | journal = Scientific American
 | pages = 120–123
 | title = Mathematical Games - The fantastic combinations of John Conway's new solitaire game "life"
 | volume = 223}}.</ref><ref>{{citation
 | last1 = Berlekamp | first1 = E. R. | author1-link = Elwyn Berlekamp
 | last2 = Conway | first2 = John Horton | author2-link = John Horton Conway
 | last3 = Guy | first3 = R.K. | author3-link = Richard K. Guy
 | edition = 2nd
 | publisher = A K Peters Ltd
 | title = [[Winning Ways for your Mathematical Plays]]
 | year = 2004}}.</ref>
|-
| B34/S34
| 34 Life
| Was initially thought to be a stable alternative to [[Conway's Game of Life|Life]], until computer simulation found that larger patterns tend to explode. Has many small oscillators and spaceships.<ref name="mirekw"/><ref>{{citation|title=The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge|first=William|last=Poundstone|page=134|publisher=Contemporary Books|year=1985|isbn=978-0-8092-5202-2}}.</ref><ref>{{citation|title=34 LIFE|first=Jack|last=Eisenmann|url=http://www.ostracodfiles.com/34life/main.html}}.</ref>
|-
| B35678/S5678
| Diamoeba
| Forms large diamonds with chaotically fluctuating boundaries. First studied by Dean Hickerson, who in 1993 offered a $50 prize to find a pattern that fills space with live cells; the prize was won in 1999 by David Bell.<ref name="mirekw"/><ref name="e10"/><ref>{{citation
 | last1 = Gravner | first1 = Janko
 | last2 = Griffeath | first2 = David
 | doi = 10.1006/aama.1998.0599
 | issue = 2
 | journal = Advances in Applied Mathematics
 | mr = 1634709
 | pages = 241–304
 | title = Cellular automaton growth on '''Z'''<sup>2</sup>: theorems, examples, and problems
 | volume = 21
 | year = 1998| doi-access = free
 }}.</ref>
|-
| B36/S125
| 2x2
| If a pattern is composed of 2x2 blocks, it will continue to evolve in the same form; grouping these blocks into larger powers of two leads to the same behavior, but slower. Has complex oscillators of high periods as well as a small glider.<ref name="mirekw"/><ref>{{citation
 | last = Johnston | first = Nathaniel
 | editor-last = Adamatzky | editor-first = Andrew | editor-link = Andrew Adamatzky
 | arxiv = 1203.1644
 | contribution = The B36/S125 "2x2" Life-Like Cellular Automaton
 | doi = 10.1007/978-1-84996-217-9_7
 | pages = 99–114
 | publisher = Springer
 | title = Game of Life Cellular Automata
 | year = 2010
 | isbn = 978-1-84996-216-2 | bibcode = 2010golc.book...99J}}.</ref>
|-
| B36/S23
| [[Highlife (cellular automaton)|HighLife]]
| Similar to Life but with a small self-replicating pattern.<ref name="mirekw"/><ref name="e10"/><ref>{{citation|url=http://www.tip.net.au/~dbell/articles/HighLife.zip|title=HighLife - An Interesting Variant of Life|first=David|last=Bell}}.</ref>
|-
| B3678/S34678
| [[Day and Night (cellular automaton)|Day & Night]]
| Symmetric under on-off reversal. Has engineered patterns with highly complex behavior.<ref name="mirekw"/><ref name="e10"/><ref>{{citation|url=http://www.tip.net.au/~dbell/articles/DayNight.zip|first=David|last=Bell|title=Day & Night - An Interesting Variant of Life}}.</ref>
|-
| B368/S245
| Morley
| Named after Stephen Morley; also called Move. Supports very high-period and slow spaceships.<ref name="mirekw"/><ref name="e10"/><ref>{{citation|url=http://safalra.com/special/b368s245/guns/|archive-url=https://web.archive.org/web/20060311051755/http://www.safalra.com/special/b368s245/guns/|url-status=dead|archive-date=2006-03-11|title=b368s245 Guns|first=Stephen|last=Morley|year=2005}}.</ref>
|-
| B4678/S35678
| Anneal
| Also called the twisted majority rule. Symmetric under on-off reversal. Approximates the [[curve-shortening flow]] on the boundaries between live and dead cells.<ref>{{citation
 | last = Vichniac | first = Gérard Y.
 | editor1-last = Bienenstock | editor1-first = E.
 | editor2-last = Fogelman Soulié | editor2-first = F.
 | editor3-last = Weisbuch | editor3-first = G.
 | contribution = Cellular automata models of disorder and organization
 | doi = 10.1007/978-3-642-82657-3_1
 | pages = 3–20
 | publisher = Springer-Verlag
 | series = NATO ASI Series
 | title = Disordered Systems and Biological Organization
 | volume = 20
 | year = 1986}}.</ref><ref>{{citation
 | last = Pickover | first = Clifford A. | authorlink = Clifford A. Pickover
 | doi = 10.1007/bf01900906
 | issue = 3
 | journal = The Visual Computer
 | pages = 173–177
 | title = Lava lamps in the 21st century
 | volume = 10
 | year = 1993}}.</ref><ref>{{citation
 | last1 = Chopard | first1 = Bastien
 | last2 = Droz | first2 = Michel
 | contribution = 2.2.4 The annealing rule
 | doi = 10.1017/CBO9780511549755
 | isbn = 0-521-46168-5
 | mr = 1669736
 | pages = 37–38
 | publisher = Cambridge University Press, Cambridge
 | series = Collection Aléa-Saclay: Monographs and Texts in Statistical Physics
 | title = Cellular automata modeling of physical systems
 | year = 1998}}.</ref>
|}

Several more rules are listed and described in the MCell rule list<ref name="mirekw"/> and by {{harvtxt|Eppstein|2010}}, including some rules with B0 in which the background of the field of cells alternates between live and dead at each step.<ref name="e10">{{citation
 | last = Eppstein | first = David | authorlink = David Eppstein
 | editor-last = Adamatzky | editor-first = Andrew | editor-link = Andrew Adamatzky
 | arxiv = 0911.2890
 | contribution = Growth and decay in {{Not a typo|life-like}} cellular automata
 | doi = 10.1007/978-1-84996-217-9_6
 | pages = 71–98
 | publisher = Springer
 | title = Game of Life Cellular Automata
 | year = 2010
 | isbn = 978-1-84996-216-2}}.</ref>

Any automaton of the above form that contains the element B1 (e.g. B17/S78, or B145/S34) will always be explosive for any finite pattern: at any step, consider the cell (''x'',''y'') that has minimum ''x''-coordinate among cells that are on, and among such cells the one with minimum ''y''-coordinate. Then the cell (''x''−1,''y''−1) must have exactly one neighbor, and will become on in the next step. Similarly, the pattern must grow at each step in each of the four diagonal directions. Thus, any nonempty starting pattern leads to explosive growth.<ref name="e10"/>

Any automaton of the above form that does not include any of B0, B1, B2 or B3 cannot support movement or expansion of patterns because any cell outside a rectangular building box containing the pattern has at most three on neighbours. Most finite patterns in rules whose notation begins with B2, and all finite patterns in rules beginning with B1, grow in all directions rather than remaining of bounded size, with a front that moves at the speed of light. Thus, the remaining "interesting" rules are the ones beginning with B3 (Game of Life, Highlife, Morley, 2x2, Day&Night) or beginning with B0 (and not including S8, as otherwise the dual can be studied instead).<ref name="e10"/>