Stability and transition in continuously deformed cellular automata

Resumen

The behavior of continuously deformed cellular automata rules is explored. The analysis is performed in terms of three entropic measures, entropy density, excess entropy, and entropy distance. These measures have been suggested to be indicative of the capabilities in the storage, processing, and transmission of information. A wealth of different behaviors is found that points to a richness of unexplored rules. Transitions can involve the loss of memory between the discrete rules at the start and end of the deformation parameter values. The behavior of the entropic measures, especially the surge of excess entropy on the verge of transition to disordered states, suggests the occurrence of enhanced computation at the edge of chaos for different types of phase transitions.