Mixed-rule Cellular Automata: Analysis of Binary Periodic Orbits and FPGA based Implementation

This paper studies binary periodic orbits in mixed-rule cellular automata (MCAs) governed by two rules of simple Boolean functions. Depending on the rules, the MCAs can generate various binary periodic orbits. In order to evaluate stability of the periodic orbits, we introduce a simple feature quantity. In order to visualize the dynamics, we introduce the digital return map. Performing fundamental numerical experiments for typical periodic orbits, we have discovered suitable rule pairs in which stability of the periodic orbit is the strongest. Application of the periodic orbits include control signal of walking robots. Presenting a simple FPGA based hardware prototype, typical periodic orbits are confirmed experimentally.