Life-like Cellular Automaton - Generalizations

Generalizations

There are other cellular automata which are inspired by the Game of Life, but which do not fit the definition of “life-like” given in this article, because their neighborhoods are larger than the Moore neighborhood, or they are defined on three-dimensional lattices, or they use a different lattice topology. For example:

• Larger than Life is a family of cellular automata studied by Kellie Michele Evans. They have very large radius neighborhoods, but perform “birth/death” thresholding similar to Conway’s life. These automata have eerily organic “glider” and “blinker” structures.

• RealLife is the “continuum limit” of Evan’s Larger Than Life CA, in the limit as the neighborhood radius goes to infinity, while the lattice spacing goes to zero. Technically, they are not cellular automata at all, because the underlying “space” is the continuous Euclidean plane R2, not the discrete lattice Z2. They have been studied by Marcus Pivato.

• Carter Bays has proposed a variety of generalizations of the Game of Life to three-dimensional CA defined on Z3. Bays has also studied two-dimensional life-like CA with triangular or hexagonal neighborhoods.