Simplifying Brownian Cellular Automata: Two States and an Average of Two Rules Per Cell

Brownian Cellular Automata (BCA) are asynchronous cellular automata in which local configurations are allowed to fluctuate in cell space. Used to drive the operations of BCA, these fluctuations facilitate a drastic reduction in the complexity of cells, with the best BCA models achieved up to now having three states and two transition rules. This paper proposes a further reduction to two states per cell, by employing cells of three different types. These three types require respectively three, two, and zero transition rules per cell. This result may bring physical implementations of BCA one step closer.