Self-reproduction in a reversible cellular space

Abstract

We investigate a problem whether self-reproduction is possible in a two-dimensional “reversible” cellular space, and give an affirmative answer. A reversible (or injective) cellular automaton (RCA) is a CA such that every configuration has at most one predecessor. In order to design an RCA we use a framework of partitioned cellular automaton (PCA). A PCA with von Neumann neighborhood is a special type of CA whose cell is divided into five parts. We designed here a reversible PCA SR 8 having 8 states in each part (thus one cell has 8 5 states). In this cellular space, encoding the shape of an object into a “gene” represented by a command sequence, copying the gene, and interpreting the gene to create an object, are all performed reversibly. We show that, by using these operations, various objects can reproduce themselves in a very simple manner.