Nonisotropic Life Game

Ryuji Takaki and Akijiro Katsu

Tokyo University of Agriculture and Technology, Fuchu, Tokyo 183, Japan

(Received October 24, 1988; Accepted August 30, 1989)

Keywords: Life Game, Nonisotropic Rule, Cellular Automata, Fractal

Abstract. The rule of the life game, a computer simulation game by Conway, is extended to allow nonisotropic weights for neighboring cells and variable evolution conditions with the aim of seeking the possibility of application to pattern formation problems in variety of fields. The conditions for survival and birth of a living cell are generalized to s₁ N s₂ and b₁ N b₂, respectively, where N is the sum of the weights of neighbors and its upper and lower bounds are specified arbitrarily. Developments of cell patterns are computed by the use of a micro-computer from several initial patterns. Modes of pattern evolution are classified as to die-out, oscillation, and growths with and without inner structure. It is found that for the isotropic rule, as in Conway's, modes of evolution are determined mainly by b₁, but in several cases with nonisotropic rule by b₁, s₂-s₁ and b₁-b₂. For some particular nonisotropic cases, appearances of interesting patterns are observed, such as Sierpinski's gasket, the spiral pattern as in the BZ reaction and turbulent spots. Effects of artificial pattern change at a certain stage of evolution and of a continuous input of random noise are also examined.