Polystate Life

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The Polystate Life family of rules is a multistate generalization of Conway's Game of Life. Polystate Life rules have one dead state and n ≥ 2 live states; each live state, along with the shared dead state, evolves according to the rules of Conway's Game of Life, independent of the remaining live states. In the event that a dead cell would get born in two or more different states simultaneously, it gets born in neither.

Polystate Life rules were developed by Boris Lejkin in April 2006.[1][2]


In n-state Life, patterns evolve according to the following rules:

  1. A live cell in state m:
    1. survives (remains live) if it has exactly 2 or 3 neighbors in state m;
    2. dies otherwise.
  2. A dead cell:
    1. gets born in state m if there is exactly one state m such that it has exactly 3 neighbors in state m;
    2. remains dead otherwise.

Software support

Polystate Life is supported in MCell using a custom DLL supplied by Nicolay Beluchenko.[2] There is no native support for Polystate Life in Golly, but custom rule tables can be used to run the Polystate Life family of rules.


Polystate Life rules can be generalized to more general classes of cellular automata, e.g. arbitrary (outer-totalistic) Life-like cellular automata, isotropic or non-isotropic cellular automata, etc. They can also be adapted to different neighborhoods, and to different tesselations of the underlying space.

Also see


  1. Boris Lejkin (2006-04-25). "Такова "Жизнь"". Retrieved on 2017-09-15.
  2. 2.0 2.1 Nicolay Beluchenko (2006-05-16). "Polystate Life". Retrieved on 2017-09-15.

External links