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

This 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.