Generations: Difference between revisions
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! Author | ! Author | ||
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| B3457/S2367/ | | B3457/S2367/C5 || 2367/3457/5 || [[Banners]] || Exploding || [[Mirek Wójtowicz]] | ||
|- | |- | ||
| B34678/S234/ | | B34678/S234/C24 || 234/34678/24 || [[Bloomerang]] || Expanding || [[John Elliott]] | ||
|- | |- | ||
| B2/S/ | | B2/S/C3 || /2/3 || [[Brian's Brain]] || Chaotic || [[Brian Silverman]] | ||
|- | |- | ||
| B378/S124567/ | | B378/S124567/C4 || 124567/378/4 || [[Caterpillars]] || Chaotic || [[Mirek Wójtowicz]] | ||
|- | |- | ||
| B2/S23/ | | B2/S23/C8 || 23/2/8 || [[Cooties]] || Exploding || [[Rudy Rucker]] | ||
|- | |- | ||
| B13/S2/ | | B13/S2/C21 || 2/13/21 || [[Fireworks]] || Exploding || [[John Elliott]] | ||
|- | |- | ||
| B34/S12/ | | B34/S12/C3 || 12/34/3 || [[Frogs]] || Chaotic || [[Scott Robert Ladd]] | ||
|- | |- | ||
| B45678/S12345/ | | B45678/S12345/C8 || 12345/45678/8 || [[Lava]] || Expanding || [[Mirek Wójtowicz]] | ||
|- | |- | ||
| B458/S012345/ | | B458/S012345/C3 || 012345/458/3 || [[Lines (CA)|Lines]] || Stable || [[Anders Starmark]] | ||
|- | |- | ||
| B2/S345/ | | B2/S345/C4 || 345/2/4 || [[Star Wars]] || Exploding || [[Mirek Wójtowicz]] | ||
|- | |- | ||
| B2/S3456/ | | B2/S3456/C6 || 3456/2/6 || [[Sticks]] || Exploding || [[Rudy Rucker]] | ||
|- | |- | ||
| B26/S345/ | | B26/S345/C5 || 345/26/5 || [[Transers]] || Exploding || [[John Elliott]] | ||
|- | |- | ||
| B2356/S1456/ | | B2356/S1456/C16 || 1456/2356/16 || [[Xtasy]] || Exploding || [[John Elliott]] | ||
|} | |} | ||
Revision as of 21:54, 22 July 2017
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.[note 1]
Description
Generations rules are described by rulestrings of the form Bx/Sy/n 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.../C2.
Examples
- Main article: List of Generations rules
| Rule (B/S/C) | Rule (S/B/C equivalent) | Name | Character | Author |
|---|---|---|---|---|
| B3457/S2367/C5 | 2367/3457/5 | Banners | Exploding | Mirek Wójtowicz |
| B34678/S234/C24 | 234/34678/24 | Bloomerang | Expanding | John Elliott |
| B2/S/C3 | /2/3 | Brian's Brain | Chaotic | Brian Silverman |
| B378/S124567/C4 | 124567/378/4 | Caterpillars | Chaotic | Mirek Wójtowicz |
| B2/S23/C8 | 23/2/8 | Cooties | Exploding | Rudy Rucker |
| B13/S2/C21 | 2/13/21 | Fireworks | Exploding | John Elliott |
| B34/S12/C3 | 12/34/3 | Frogs | Chaotic | Scott Robert Ladd |
| B45678/S12345/C8 | 12345/45678/8 | Lava | Expanding | Mirek Wójtowicz |
| B458/S012345/C3 | 012345/458/3 | Lines | Stable | Anders Starmark |
| B2/S345/C4 | 345/2/4 | Star Wars | Exploding | Mirek Wójtowicz |
| B2/S3456/C6 | 3456/2/6 | Sticks | Exploding | Rudy Rucker |
| B26/S345/C5 | 345/26/5 | Transers | Exploding | John Elliott |
| B2356/S1456/C16 | 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
Generations rules can, in a straightforward manner, be adapted to von Neumann and hexagonal neighbourhoods and extended to non-totalistic and non-isotropic rules.
Larger than Life rules extend Generations rules to larger neighbourhoods.
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.
External links
Generations at Golly's online help Family: Generations at Mirek Wójtowicz's Cellebration page