Evolution and Dynamics of Small-World Cellular Automata

We study an extension of cellular automata to arbitrary interconnection topologies for the majority and the synchronization problems. By using an evolutionary algorithm, we show that small-world type network topologies consistently evolve from regular and random structures without being designed beforehand. These topologies have better performance than regular lattice structures and are easier to evolve, which could explain in part their ubiquity. Moreover, we show experimentally that general graph topologies are much more robust in the face of random faults than lattice structures for these problems.