On two integrable cellular automata

From Discrete Integrable Systems to Cellular Automata

Two-Dimensional Cellular Automata

A largely phenomenological study of two-dimensional cellular automata is reported. Qualitative classes of behavior similar to those in one-dimensional cellular automata are found. Growth from simple seeds in two-dimensional cellular automata can produce patterns with complicated boundaries, characterized by a variety of growth dimensions. Evolutionfrom disordered states can give domains with bo...

Two-Dimensional Cellular Automata

A largely phenomenological study of two-dimensional cellular automata is reported. Qualitative classes of behavior similar to those in one-dimensional cellular automata are found. Growth from simple seeds in two-dimensional cellular automata can produce patterns with complicated boundaries, characterized by a variety of growth dimensions. Evolution from disordered states can give domains with b...

Two-player games on cellular automata

Cellular automata games have traditionally been 0-player or solitaire games. We define a two-player cellular automata game played on a finite cyclic digraph G = (V, E). Each vertex assumes a weight w ∈ {0, 1}. A move consists of selecting a vertex u with w(u) = 1 and firing it, i.e., complementing its weight and that of a selected neighborhood of u. The player first making all weights 0 wins, a...

Two-Dimensional Cellular Automata Synchronizers

We study a firing squad synchronization problem that gives a finite-state protocol for synchronizing large-scale cellular automata. In this paper, we give a survey on recent developments in designing optimumand non-optimum-time synchronization algorithms and present their state-efficient implementations for two-dimensional cellular arrays. Several simple, state-efficient mapping schemes are pro...