Constructibility of signal-crossing solutions in von Neumann 29-state cellular automata

Abstract

In von Neumann 29-state cellular automata, the crossing of signals is an important problem, with three solutions reported in the literature. These solutions greatly impact automaton design, especially self-replicators. This paper examines these solutions, with emphasis upon their constructibility. We show that two of these solutions are difficult to construct, and offer an improved design technique. We also argue that solutions to the signal-crossing problem have implications for machine models of biological development, especially with regard to the cell cycle. © Springer-Verlag Berlin Heidelberg 2005.