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{{Glossary}}
{{Glossary}}
'''Generations''' rules (or '''multistate rules''') are a generalization of [[Life-like cellular automata]] in which live cells can exist in different states, and cells that would die in a 2-state cellular automaton instead advance to the next state. The name "Generations" is due to the conceptualization of this process as cells "getting older" before eventually dying.{{refn|group=note|The name "Generations", and the different states in which cells in Generations rules can exist, should not be confused with the generations (i.e. repeated evolution) of a pattern.}}
'''Generations''' rules are a [[multistate rule|multistate]] generalization of [[Life-like cellular automata]] in which live cells can exist in different states, and cells that would die in a 2-state cellular automaton instead advance to the next state.  


==Description==
The name "Generations" is due to the conceptualization of this process as cells "getting older" before eventually dying.{{refn|group=note|The name "Generations", and the different states in which cells in Generations rules can exist, should not be confused with the generations (i.e. repeated evolution) of a pattern.}}
Generations rules are described by [[rulestring]]s of the form <tt>Bx/Sy/Cn</tt>{{refn|group=note|"C" stands for "Count" (of cell states); alternatively, "G" (for "Generations") may be used.}} or <tt>y/x/n</tt>, an extension of B/S and S/B rulestrings where ''n'' is any natural number &ge;2. Patterns evolve according to the following rules:
 
== Description ==
Generations rules are described by [[rulestring]]s of the form <tt>Bx/Sy/n</tt>{{refn|group=note|<tt>Bx/Sy/Cn</tt> and <tt>Bx/Sy/Gn</tt> are also sometimes used, with "C" standing for "Count" (of cell states), and "G" for "Generations". If "C" is used, care must be taken to not confuse the state count with a [[symmetry]], e.g. "B3/S23/C4".}} or <tt>y/x/n</tt>, an extension of B/S and S/B rulestrings where ''n'' is any natural number &ge;2. Patterns evolve according to the following rules:


# A cell in state 0 ("dead") will advance to state 1 ("get born") in the next generation of the pattern if the number of neighbors in state 1 ("live") in its [[Moore neighbourhood]] is present in the rule's birth conditions (<tt>Bx</tt>).
# A cell in state 0 ("dead") will advance to state 1 ("get born") in the next generation of the pattern if the number of neighbors in state 1 ("live") in its [[Moore neighbourhood]] is present in the rule's birth conditions (<tt>Bx</tt>).
Line 11: Line 13:
# A cell in state ''m'' &ge; 2 will advance to state ''((m + 1)'' mod ''n)'' in the next generation of the pattern. In particular, a cell in state ''n'' will reset to state 0 ("die").
# A cell in state ''m'' &ge; 2 will advance to state ''((m + 1)'' mod ''n)'' in the next generation of the pattern. In particular, a cell in state ''n'' will reset to state 0 ("die").


Any [[outer-totalistic Life-like cellular automaton]] with rulestring <tt>B.../S...</tt> is equivalent to the Generations rule with rulestring <tt>B.../S.../C2</tt>.
Any [[outer-totalistic cellular automaton]] with rulestring <tt>B.../S...</tt> is equivalent to the Generations rule with rulestring <tt>B.../S.../2</tt>.
 
B0 is also possible for Generations rules, however software support is not widespread.


==Examples==
== Examples ==
{{Main|List of Generations rules}}
{{Main|List of Generations rules}}


Line 24: Line 28:
! Author
! Author
|-
|-
| B3457/S2367/C5 || 2367/3457/5 || [[Banners]] || Exploding || [[Mirek Wójtowicz]]
| B34578/S237/4 || 345678/237/4 || {{rl|9:43 at Knight}} || Stable || [[EricG]]
|-
| B3457/S2367/5 || 2367/3457/5 || {{rl|Banners}} || Exploding || [[Mirek Wójtowicz]]
|-
|-
| B34678/S234/C24 || 234/34678/24 || [[Bloomerang]] || Expanding || [[John Elliott]]
| B34678/S234/24 || 234/34678/24 || {{rl|Bloomerang}} || Expanding || [[John Elliott]]
|-
|-
| B2/S/C3 || /2/3 || [[Brian's Brain]] || Chaotic || [[Brian Silverman]]
| B246/S6/3 || 6/2/3 || {{rl|Brian 6}} || Chaotic || [[Michael Sweney]]
|-
|-
| B378/S124567/C4 || 124567/378/4 || [[Caterpillars]] || Chaotic || [[Mirek Wójtowicz]]
| B2/S/3 || /2/3 || {{rl|Brian's Brain}} || Chaotic || [[Brian Silverman]]
|-
|-
| B2/S23/C8 || 23/2/8 || [[Cooties]] || Exploding || [[Rudy Rucker]]
| B378/S124567/4 || 124567/378/4 || {{rl|Caterpillars}} || Chaotic || [[Mirek Wójtowicz]]
|-
|-
| B13/S2/C21 || 2/13/21 || [[Fireworks]] || Exploding || [[John Elliott]]
| B2/S23/8 || 23/2/8 || {{rl|Cooties}} || Exploding || [[Rudy Rucker]]
|-
|-
| B34/S12/C3 || 12/34/3 || [[Frogs]] || Chaotic || [[Scott Robert Ladd]]
| B13/S2/21 || 2/13/21 || {{rl|Fireworks}} || Exploding || [[John Elliott]]
|-
|-
| B45678/S12345/C8 || 12345/45678/8 || [[Lava]] || Expanding || [[Mirek Wójtowicz]]
| B34/S12/3 || 12/34/3 || {{rl|Frogs}} || Chaotic || [[Scott Robert Ladd]]
|-
|-
| B458/S012345/C3 || 012345/458/3 || [[Lines (CA)|Lines]] || Stable || [[Anders Starmark]]
| B45678/S12345/8 || 12345/45678/8 || {{rl|Lava}} || Expanding || [[Mirek Wójtowicz]]
|-
|-
| B2/S345/C4 || 345/2/4 || [[Star Wars]] || Exploding || [[Mirek Wójtowicz]]
| B458/S012345/3 || 012345/458/3 || {{rl|Lines}} || Stable || [[Anders Starmark]]
|-
|-
| B2/S3456/C6 || 3456/2/6 || [[Sticks]] || Exploding || [[Rudy Rucker]]
| B2/S345/4 || 345/2/4 || {{rl|Star Wars}} || Exploding || [[Mirek Wójtowicz]]
|-
|-
| B26/S345/C5 || 345/26/5 || [[Transers]] || Exploding || [[John Elliott]]
| B2/S3456/6 || 3456/2/6 || {{rl|Sticks}} || Exploding || [[Rudy Rucker]]
|-
|-
| B2356/S1456/C16 || 1456/2356/16 || [[Xtasy]] || Exploding || [[John Elliott]]
| B26/S345/5 || 345/26/5 || {{rl|Transers}} || Exploding || [[John Elliott]]
|-
| B2356/S1456/16 || 1456/2356/16 || {{rl|Xtasy}} || Exploding || [[John Elliott]]
|}
|}


==Software support==
== Software support ==
Both [[MCell]] and [[Golly]] support Generations rules, the latter with a maximum of 256 states. Generations rules are also supported by [[User:rowett|Chris Rowett]]'s [[LifeViewer]] starting with build 180.
Both [[MCell]] and [[Golly]] support Generations rules, the latter with a maximum of 256 states. Golly currently does not support Generations rules with B0; a method of emulating such rules was added in beta versions of Golly 2.9, but was ultimately scrapped due to bugs and complexity.<ref>https://conwaylife.com/forums/viewtopic.php?f=7&t=4133&p=88707#p88734</ref> Non-B0 Generations rules are also supported by [[Chris Rowett]]'s [[LifeViewer]] starting with build 180.


==Extensions==
[[CAViewer]] can support Generations rules including those with B0.
Generations rules can, in a straightforward manner, be adapted to [[von Neumann neighbourhood|von Neumann]] and [[hexagonal neighbourhood|hexagonal]] neighbourhoods and extended to [[non-totalistic Life-like cellular automaton|non-totalistic]] and [[non-isotropic Life-like cellular automaton|non-isotropic]] rules.
 
== Extensions and variants ==
Generations rules can, in a straightforward manner, be adapted to [[von Neumann neighbourhood|von Neumann]], [[hexagonal neighbourhood|hexagonal]] and [[triangular neighbourhood|triangular]] neighbourhoods and extended to [[non-totalistic cellular automaton|non-totalistic]] and [[non-isotropic cellular automaton|non-isotropic]] rules.


[[Larger than Life]] rules extend Generations rules to larger neighbourhoods.
[[Larger than Life]] rules extend Generations rules to larger neighbourhoods.


So-called "snoitareneG" rules, in which cells take time to become alive, have been explored.<ref name="thread2939" />
Reverse Generations rules (also called "snoitareneG" rules), in which cells take time to become alive, have been explored.<ref name="thread372" /><ref name="post44058" /><ref name="thread2939" /> These are not directly supported by Golly or [[apgsearch]], although [[ruletable]]s have been used for the former.


==Notes==
Generation and snoitareneG can be considered subsets of the [[Extended Generations]] rulespace,<ref name="post62255" /> which is supported by apgsearch.
 
== See also ==
* [[BSFKL]]
* [[Larger than Life]]
* [[Neutronium]]
 
== Notes ==
<references group="note" />
<references group="note" />


==References==
== References ==
<references>
<references>
<ref name="thread2939">{{LinkForumThread|
<ref name="thread372">{{LinkForumThread
|title  = "Reverse Generations" Rules
|format = ref
|t      = 372
|author = Martin Grant
|date  = April 10, 2010
}}</ref>
<ref name="thread2939">{{LinkForumThread
|title  = snoitareneG Rules
|title  = snoitareneG Rules
|format = ref
|format = ref
|t      = 2939
|t      = 2939
|author = Saka
|date  = July 2, 2017
}}</ref>
<ref name="post44058">{{LinkForumThread
|title  = Re: Thread for basic questions
|author = Brian Prentice
|date  = June 4, 2017
|format = ref
|p      = 44058
|t      = 2036
|f      = 7
}}</ref>
<ref name="post62255">{{LinkForumThread
|format = ref
|title  = "Extended" Generations rules
|p      = 62255
|author = M. I. Wright
|date  = August 1, 2018
}}</ref>
}}</ref>
</references>
</references>


==External links==
== External links ==
{{LinkGollyHelp|filename=Algorithms/Generations.html|title=Generations}}
* {{LinkGollyHelp|filename=Algorithms/Generations.html|title=Generations}}
{{LinkMirek|rullex_gene.html|title=Family: Generations}}
* {{LinkMirek|rullex_gene.html|title=Family: Generations}}


[[Category:Algorithms]]
[[Category:Algorithms]]
[[Category:Cellular automata]]
[[Category:Cellular automata]]
[[Category:Generations| ]]

Latest revision as of 07:39, 27 August 2025

Generations rules are a multistate generalization of Life-like cellular automata in which live cells can exist in different states, and cells that would die in a 2-state cellular automaton instead advance to the next state.

The name "Generations" is due to the conceptualization of this process as cells "getting older" before eventually dying.[note 1]

Description

Generations rules are described by rulestrings of the form Bx/Sy/n[note 2] or y/x/n, an extension of B/S and S/B rulestrings where n is any natural number ≥2. Patterns evolve according to the following rules:

  1. A cell in state 0 ("dead") will advance to state 1 ("get born") in the next generation of the pattern if the number of neighbors in state 1 ("live") in its Moore neighbourhood is present in the rule's birth conditions (Bx).
  2. A cell in state 1 ("live") will:
    1. Remain in state 1 ("survive") in the next generation of the pattern if the number of neighbors in state 1 ("live") in its Moore neighborhood is present in the rule's survival conditions (Sx).
    2. Advance to state 2 ("age") in the next generation of the pattern otherwise.
  3. A cell in state m ≥ 2 will advance to state ((m + 1) mod n) in the next generation of the pattern. In particular, a cell in state n will reset to state 0 ("die").

Any outer-totalistic cellular automaton with rulestring B.../S... is equivalent to the Generations rule with rulestring B.../S.../2.

B0 is also possible for Generations rules, however software support is not widespread.

Examples

Main article: List of Generations rules
Rule (B/S/C) Rule (S/B/C equivalent) Name Character Author
B34578/S237/4 345678/237/4 9:43 at Knight Stable EricG
B3457/S2367/5 2367/3457/5 Banners Exploding Mirek Wójtowicz
B34678/S234/24 234/34678/24 Bloomerang Expanding John Elliott
B246/S6/3 6/2/3 Brian 6 Chaotic Michael Sweney
B2/S/3 /2/3 Brian's Brain Chaotic Brian Silverman
B378/S124567/4 124567/378/4 Caterpillars Chaotic Mirek Wójtowicz
B2/S23/8 23/2/8 Cooties Exploding Rudy Rucker
B13/S2/21 2/13/21 Fireworks Exploding John Elliott
B34/S12/3 12/34/3 Frogs Chaotic Scott Robert Ladd
B45678/S12345/8 12345/45678/8 Lava Expanding Mirek Wójtowicz
B458/S012345/3 012345/458/3 Lines Stable Anders Starmark
B2/S345/4 345/2/4 Star Wars Exploding Mirek Wójtowicz
B2/S3456/6 3456/2/6 Sticks Exploding Rudy Rucker
B26/S345/5 345/26/5 Transers Exploding John Elliott
B2356/S1456/16 1456/2356/16 Xtasy Exploding John Elliott

Software support

Both MCell and Golly support Generations rules, the latter with a maximum of 256 states. Golly currently does not support Generations rules with B0; a method of emulating such rules was added in beta versions of Golly 2.9, but was ultimately scrapped due to bugs and complexity.[1] Non-B0 Generations rules are also supported by Chris Rowett's LifeViewer starting with build 180.

CAViewer can support Generations rules including those with B0.

Extensions and variants

Generations rules can, in a straightforward manner, be adapted to von Neumann, hexagonal and triangular neighbourhoods and extended to non-totalistic and non-isotropic rules.

Larger than Life rules extend Generations rules to larger neighbourhoods.

Reverse Generations rules (also called "snoitareneG" rules), in which cells take time to become alive, have been explored.[2][3][4] These are not directly supported by Golly or apgsearch, although ruletables have been used for the former.

Generation and snoitareneG can be considered subsets of the Extended Generations rulespace,[5] which is supported by apgsearch.

See also

Notes

  1. ↑ The name "Generations", and the different states in which cells in Generations rules can exist, should not be confused with the generations (i.e. repeated evolution) of a pattern.
  2. ↑ Bx/Sy/Cn and Bx/Sy/Gn are also sometimes used, with "C" standing for "Count" (of cell states), and "G" for "Generations". If "C" is used, care must be taken to not confuse the state count with a symmetry, e.g. "B3/S23/C4".

References

  1. ↑ https://conwaylife.com/forums/viewtopic.php?f=7&t=4133&p=88707#p88734
  2. ↑ Martin Grant (April 10, 2010). "Reverse Generations" Rules (discussion thread) at the ConwayLife.com forums
  3. ↑ Brian Prentice (June 4, 2017). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
  4. ↑ Saka (July 2, 2017). snoitareneG Rules (discussion thread) at the ConwayLife.com forums
  5. ↑ M. I. Wright (August 1, 2018). "Extended" Generations rules (discussion thread) at the ConwayLife.com forums
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