CIRCUIT IMPLEMENTATION OF HISTORIC ANALOG CELLULAR AUTOMATA BASED ON WOLFRAM’S RULES 90 AND 150

Standard cellular automata (CA) employes transition rules where a cell’s state is updated in terms of the previous state (1 step before) of the cell’s neighbors. This standard framework has recently been expanded by introducing historic memory capabilities into CAs, i.e., a cell’s state is updated by not only the neighbor’s previous state but also the past states (2, 3,..., M steps before), which resulted in generating statistically good random numbers [1], spatialized prisoner’s dilemma [2], multi-fractal properties of Wolfram’s rule 90 [3], and so on. We here propose semi-analog CAs based on Wolfram’s rules 90 and 150 having historic memory capabilities. Original difference equations of 1-D CAs with rules 90 and 150 are given by xt+1i = f(x t i−1,