Polystate Life

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 Boris Lejkin in April 2006.

Description

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.

Extensions

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

• Colourised Life

External links

• Lejkin's Polystate Life (discussion thread) at the ConwayLife.com forums