Complex Systems

Max-Plus Generalization of Conway’s Game of Life Download PDF

Kotaro Sakata
Yuta Tanaka
Daisuke Takahashi *

Department of Pure and Applied Mathematics, Waseda University
3-4-1, Okubo, Shinjuku-ku
Tokyo, 169-8555, Japan


We propose a max-plus equation that includes Conway’s Game of Life (GoL) as a special case. There are some special solutions to the equation that include and unify solutions to GoL. Moreover, the multivalue extension of GoL is derived from the equation, and the behavior of solutions is discussed.

Keywords: cellular automaton; Conway’s Game of Life; max-plus equation

Cite this publication as:
K. Sakata, Y. Tanaka and D. Takahashi, “Max-Plus Generalization of Conway’s Game of Life,” Complex Systems, 29(1), 2020 pp. 63–76.