Are Some Family Members Harmful? – A Study on Diploid Cellular Automata

This paper explores diploid elementary cellular automata (ECA) systems where the rules of the cellular systems are acquired with a random mixing of two ECAs. However, here, we consider two ECAs from the same family following left to right, 0 to 1, and both transformations. Following the experimental approach, this study classifies the dynamics of (all possible) 300 diploid family couples following Wolfram’s and Li and Packard’s classification. We investigate the resistance of this diploid system against this family perturbation. As we will see, this study is interesting enough to provide the following rich phenomenon: (1) two-periodic family couple together show chaotic dynamics and vice-versa; (2) some diploid couple changes their class dynamics after a critical value of mixing rate, i.e. class transition; and (3) lastly, these diploid couples are also capable to show continuous or second-order phase transition dynamics.