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]
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.
- Main article: List of Generations rules
|Rule (B/S/C)||Rule (S/B/C equivalent)||Name||Character||Author|
|B2/S/3||/2/3||Brian's Brain||Chaotic||Brian Silverman|
|B34/S12/3||12/34/3||Frogs||Chaotic||Scott Robert Ladd|
|B2/S345/4||345/2/4||Star Wars||Exploding||Mirek Wójtowicz|
Extensions and variants
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. 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, which is supported by apgsearch.
- 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".
- "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