Effect of family noise in Diploid Cellular Automata

This paper explores diploid elementary cellular automata (ECA) systems where the rules of the cellular automata (CA) are acquired with a random mixing of two elementary CA rules. However, here, we consider two ECA rules from the same family following left to right, 0 to 1, and both transformation. Following the qualitative (i.e., space-time pictures) and quantitative (i.e., density, activity, and Kolmogorov-Sinai entropy) experimental approach, this study classifies the dynamics of (all possible) 300 family diploid couples after considering Wolfram’s and Li and Packard’s classification. According to the results, some family diploid couples show strong resistance against this proposed family noise, i.e., robust class. However, as we will see, this study is interesting enough to provide following rich phenomenon: (1) Two periodic or locally chaotic ECA rules together as a family couple show completely opposite chaotic dynamics and vice versa; (2) There is evidence of diploid couples where we are not able to classify the dynamics of the system following only Wolfram’s and Li-Packard’s classes. In this context, we introduce the notion of following new classes-Noise and Periodic dynamics with more complexity; (3) Moreover, these family diploid couples are also capable to show continuous or second-order phase transition dynamics along with the evidence of abrupt phase transition dynamics; and (4) Lastly, some diploid couples change their class dynamics after a critical value of family noise rate, i.e, class transition dynamics. According to the results, the proposed family diploid systems show both abrupt and continuous class transition dynamics.