Difference between revisions of "Generations"
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{{Glossary}} | {{Glossary}} | ||
'''Generations''' 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. | ||
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> 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: | ||
# 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>). | ||
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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 Life-like cellular automaton]] with rulestring <tt>B.../S...</tt> is equivalent to the Generations rule with rulestring <tt>B.../S.../ | Any [[outer-totalistic Life-like cellular automaton]] with rulestring <tt>B.../S...</tt> is equivalent to the Generations rule with rulestring <tt>B.../S.../2</tt>. | ||
==Examples== | ==Examples== | ||
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| B45678/S12345/8 || 12345/45678/8 || [[Lava]] || Expanding || [[Mirek Wójtowicz]] | | B45678/S12345/8 || 12345/45678/8 || [[Lava]] || Expanding || [[Mirek Wójtowicz]] | ||
|- | |- | ||
| B458/S012345/3 || 012345/458/3 || [[Lines ( | | B458/S012345/3 || 012345/458/3 || [[Lines (rule)|Lines]] || Stable || [[Anders Starmark]] | ||
|- | |- | ||
| B2/S345/4 || 345/2/4 || [[Star Wars]] || Exploding || [[Mirek Wójtowicz]] | | B2/S345/4 || 345/2/4 || [[Star Wars]] || Exploding || [[Mirek Wójtowicz]] | ||
| Line 52: | Line 54: | ||
==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 [[Chris Rowett]]'s [[LifeViewer]] starting with build 180. | 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. | ||
==Extensions== | ==Extensions and variants== | ||
Generations rules can, in a straightforward manner, be adapted to [[von Neumann neighbourhood|von Neumann]] | 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 Life-like cellular automaton|non-totalistic]] and [[non-isotropic Life-like 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 ruletables 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. | |||
==See also== | |||
* [[BSFKL]] | |||
* [[Larger than Life]] | |||
* [[List of rules investigated on Catagolue#Generations rules|List of Generations rules investigated on Catagolue]] | |||
==Notes== | ==Notes== | ||
<references group="note" /> | <references group="note" /> | ||
==References== | |||
<references> | |||
<ref name="thread372">{{LinkForumThread | |||
|title = "Reverse Generations" Rules | |||
|format = ref | |||
|t = 372 | |||
}}</ref> | |||
<ref name="thread2939">{{LinkForumThread | |||
|title = snoitareneG Rules | |||
|format = ref | |||
|t = 2939 | |||
}}</ref> | |||
<ref name="post44058">{{LinkForumThread | |||
|title = Re: Thread for basic questions | |||
|author = Brian Prentice | |||
|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> | |||
</references> | |||
==External links== | ==External links== | ||
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[[Category:Algorithms]] | [[Category:Algorithms]] | ||
[[Category:Cellular automata]] | |||
[[Category:Generations| ]] | |||
Revision as of 15:59, 18 August 2019
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 Life-like cellular automaton with rulestring B.../S... is equivalent to the Generations rule with rulestring B.../S.../2.
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. Generations rules are also supported by Chris Rowett's LifeViewer starting with build 180.
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.[1][2][3] 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,[4] 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
- ↑ "Reverse Generations" Rules (discussion thread) at the ConwayLife.com forums
- ↑ Brian Prentice. Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
- ↑ 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