2015•Revista de la Unión Matemática ArgentinaOpen access

A note on the reversibility of the elementary cellular automaton with rule number 90

A. Martı́n del Rey

Abstract

The reversibility properties of the elementary cellular automaton with rule number 90 are studied. It is shown that the cellular automaton considered is not reversible when periodic boundary conditions are considered, whereas when null boundary conditions are stated, the reversibility appears when the number of cells of the cellular space is even. The DETGTRI algorithm is used to prove these statements. Moreover, the explicit expressions of inverse cellular automata of reversible ones are computed.

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Key concepts: Cellular automaton, Elementary cellular automaton, Stochastic cellular automaton, Block cellular automaton, Reversible cellular automaton, Boundary (topology), Mathematics, Continuous automaton