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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.}} | 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.}} | ||
==Description== | == 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 ≥2. Patterns evolve according to the following rules: | 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 ≥2. Patterns evolve according to the following rules: | ||
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# 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"). | # 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 | Any [[outer-totalistic cellular automaton]] with rulestring <tt>B.../S...</tt> is equivalent to the Generations rule with rulestring <tt>B.../S.../2</tt>. | ||
==Examples== | B0 is also possible for Generations rules, however software support is not widespread. | ||
== Examples == | |||
{{Main|List of Generations rules}} | {{Main|List of Generations rules}} | ||
| Line 26: | Line 28: | ||
! Author | ! Author | ||
|- | |- | ||
| B3457/S2367/5 || 2367/3457/5 || | | B3457/S2367/5 || 2367/3457/5 || {{rl|Banners}} || Exploding || [[Mirek Wójtowicz]] | ||
|- | |- | ||
| B34678/S234/24 || 234/34678/24 || | | B34678/S234/24 || 234/34678/24 || {{rl|Bloomerang}} || Expanding || [[John Elliott]] | ||
|- | |- | ||
| B2/S/3 || /2/3 || | | B2/S/3 || /2/3 || {{rl|Brian's Brain}} || Chaotic || [[Brian Silverman]] | ||
|- | |- | ||
| B378/S124567/4 || 124567/378/4 || | | B378/S124567/4 || 124567/378/4 || {{rl|Caterpillars}} || Chaotic || [[Mirek Wójtowicz]] | ||
|- | |- | ||
| B2/S23/8 || 23/2/8 || | | B2/S23/8 || 23/2/8 || {{rl|Cooties}} || Exploding || [[Rudy Rucker]] | ||
|- | |- | ||
| B13/S2/21 || 2/13/21 || | | B13/S2/21 || 2/13/21 || {{rl|Fireworks}} || Exploding || [[John Elliott]] | ||
|- | |- | ||
| B34/S12/3 || 12/34/3 || | | B34/S12/3 || 12/34/3 || {{rl|Frogs}} || Chaotic || [[Scott Robert Ladd]] | ||
|- | |- | ||
| B45678/S12345/8 || 12345/45678/8 || | | B45678/S12345/8 || 12345/45678/8 || {{rl|Lava}} || Expanding || [[Mirek Wójtowicz]] | ||
|- | |- | ||
| B458/S012345/3 || 012345/458/3 || | | B458/S012345/3 || 012345/458/3 || {{rl|Lines}} || Stable || [[Anders Starmark]] | ||
|- | |- | ||
| B2/S345/4 || 345/2/4 || | | B2/S345/4 || 345/2/4 || {{rl|Star Wars}} || Exploding || [[Mirek Wójtowicz]] | ||
|- | |- | ||
| B2/S3456/6 || 3456/2/6 || | | B2/S3456/6 || 3456/2/6 || {{rl|Sticks}} || Exploding || [[Rudy Rucker]] | ||
|- | |- | ||
| B26/S345/5 || 345/26/5 || | | B26/S345/5 || 345/26/5 || {{rl|Transers}} || Exploding || [[John Elliott]] | ||
|- | |- | ||
| B2356/S1456/16 || 1456/2356/16 || | | 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 [[ | 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. | ||
[[CAViewer]] can support Generations rules including those with B0. | |||
==Extensions and variants== | == 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 | 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. | ||
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 | 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. | ||
Generation and snoitareneG can be considered subsets of the [[Extended Generations]] rulespace,<ref name="post62255" /> which is supported by apgsearch. | Generation and snoitareneG can be considered subsets of the [[Extended Generations]] rulespace,<ref name="post62255" /> which is supported by apgsearch. | ||
==See also== | == See also == | ||
* [[BSFKL]] | * [[BSFKL]] | ||
* [[Larger than Life]] | * [[Larger than Life]] | ||
* [[ | * [[Neutronium]] | ||
==Notes== | == Notes == | ||
<references group="note" /> | <references group="note" /> | ||
==References== | == References == | ||
<references> | <references> | ||
<ref name="thread372">{{LinkForumThread | <ref name="thread372">{{LinkForumThread | ||
| Line 108: | Line 111: | ||
</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| ]] | [[Category:Generations| ]] | ||
Latest revision as of 15:03, 7 March 2023
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:
- 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).
- A cell in state 1 ("live") will:
- 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).
- Advance to state 2 ("age") in the next generation of the pattern otherwise.
- 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 |
|---|---|---|---|---|
| B3457/S2367/5 | 2367/3457/5 | Banners | Exploding | Mirek Wójtowicz |
| B34678/S234/24 | 234/34678/24 | Bloomerang | Expanding | John Elliott |
| 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
- ↑ 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.
- ↑ 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
- ↑ https://conwaylife.com/forums/viewtopic.php?f=7&t=4133&p=88707#p88734
- ↑ Martin Grant (April 10, 2010). "Reverse Generations" Rules (discussion thread) at the ConwayLife.com forums
- ↑ Brian Prentice (June 4, 2017). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
- ↑ Saka (July 2, 2017). snoitareneG Rules (discussion thread) at the ConwayLife.com forums
- ↑ M. I. Wright (August 1, 2018). "Extended" Generations rules (discussion thread) at the ConwayLife.com forums
External links
- Generations at Golly's online help
- Family: Generations at Mirek Wójtowicz's Cellebration page