An 8-state simple reversible triangular cellular automaton that exhibits complex behavior

Abstract

A three-neighbor triangular partitioned cellular automaton (TPCA) is a CA whose cell is triangular-shaped and divided into three parts. The next state of a cell is determined by the three adjacent parts of its neighbor cells. The framework of TPCA makes it easy to design reversible triangular CAs. Among them, isotropic 8-state (i.e., each part has two states) TPCAs, which are called elementary TPCAs (ETPCAs), are extremely simple, since each of their local transition functions is described by only four local rules. In this paper, we investigate a specific reversible ETPCA T0347, where 0347 is its identification number in the class of 256 ETPCAs. In spite of the simplicity of the local function and the constraint of reversibility, evolutions of configurations in T0347 have very rich varieties, and look like those in the Game-of-Life CA to some extent. In particular, a “glider” and “glider guns” exist in T0347. Furthermore, using gliders to represent signals, we can implement universal reversible logic gates in it. By this, computational universality of T0347 is derived.