Generations

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 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/S2367/52367/3457/5BannersExplodingMirek Wójtowicz
B34678/S234/24234/34678/24BloomerangExpandingJohn Elliott
B2/S/3/2/3Brian's BrainChaoticBrian Silverman
B378/S124567/4124567/378/4CaterpillarsChaoticMirek Wójtowicz
B2/S23/823/2/8CootiesExplodingRudy Rucker
B13/S2/212/13/21FireworksExplodingJohn Elliott
B34/S12/312/34/3FrogsChaoticScott Robert Ladd
B45678/S12345/812345/45678/8LavaExpandingMirek Wójtowicz
B458/S012345/3012345/458/3LinesStableAnders Starmark
B2/S345/4345/2/4Star WarsExplodingMirek Wójtowicz
B2/S3456/63456/2/6SticksExplodingRudy Rucker
B26/S345/5345/26/5TransersExplodingJohn Elliott
B2356/S1456/161456/2356/16XtasyExplodingJohn 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.

gollark: No. We use base 10 here.
gollark: #8 has votes on it already, and I don't THINK they should retroactively apply.
gollark: I was very wise and foresighted, you see.
gollark: I definitely noticed that and did not foolishly assume you hadn't edited it to say zero instead of one.
gollark: We voted democracyicially to be unable to vote for things.

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. Martin Grant (April 10, 2010). "Reverse Generations" Rules (discussion thread) at the ConwayLife.com forums
  2. Brian Prentice (June 4, 2017). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
  3. Saka (July 2, 2017). snoitareneG Rules (discussion thread) at the ConwayLife.com forums
  4. M. I. Wright (August 1, 2018). "Extended" Generations rules (discussion thread) at the ConwayLife.com forums
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