The extended glider-eater machine in the spiral rule

Abstract

We investigate the glider-eater interaction in a 2-dimensional reaction-diffusion cellular automaton, the Adamatzky-Wuensche Spiral Rule. We present the complete state transition table of such interactions, with which one can build the extended glider-eater machine composed of multiple instances of gliders and eaters to compute in specific problems. We demonstrate the implementation of asynchronous counters with the extended glider-eater machine. Since the counter can be understood as a part of the Minsky register machine with only the INC (increment) function implemented, we envisage that the extended glider-eater machine could be essential if one intends to build a complete Minsky register machine in the Spiral Rule and to prove the rule is Turing-universal. © Springer-Verlag Berlin Heidelberg 2010.