Hyperplane localisation of self-replicating and other complex cellular automata rules

We study the regions of cellular automata rule-space in which interesting, so-called complex, rules arise. Particularly interesting structures are self-replicators, arising from initial random conditions. In order to find the critical region, we develop a parameterisation of the cellular automata rule-space. The results clearly identify an abrupt transition between order and chaos, in the proximity of critical parameters values, in which complex systems are likely to be found