Copy Machines-Self-reproduction with 2 States on Archimedean Tilings

Abstract

Self-reproducing feature of cellular automata is one of the most important aim from the beginnings. In this article we show binary (2-state) infinite grid self-reproducing automata which reproduce (few copies) of the original pattern in various grids. For the three regular grids we prove their behavior based on path-counting. Similar machine also works on many semi-regular tilings. Moreover, we show that in some stage, by removing the copies and keeping only central embryo part of the pattern, it is able to reconstruct the pattern to be copied. To illustrate the self-reproduction various patterns are reproduced in various tessellations.