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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:

  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.


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 and hexagonal 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 supported by Golly or apgsearch, although ruletables have been used for the former.

Also see


  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".


  1. "Reverse Generations" Rules (discussion thread) at the forums
  2. Brian Prentice. Re: Thread for basic questions (discussion thread) at the forums
  3. snoitareneG Rules (discussion thread) at the forums

External links