Three‐state neumann neighbor cellular automata capable of constructing self‐reproducing machines

Abstract

AbstractThis paper defines the 3‐state Neumann‐neighbor cellular automata, and shows that its space is construction‐universal. The proof for this is achieved by presenting a realization of self‐reproducing machines. The state‐transition rule and the basic operations of configurations of the cellular automata are described first. Then methods are shown to construct AND circuit, pulse generator, signal‐line, delay circuit and memory circuit. Finally, the structure of the self‐reproducing machine is shown, which is realized by combining those circuits, The machine has two construction arms, a Turing tape and a timing loop. It can make a replica of its own using the Turing tape. The machine can also be operated as a universal construction machine or a universal Turing machine.