A Note on Skew-Asynchronous Cellular Automata

Atomicity property (in other words, fully asynchronism) is a well-studied source of the noise or perturbation in cellular systems where two consecutive cells are not allowed to be updated simultaneously. In this work, we question this restriction and introduce the notion of skewed environment where atomicity property is not respected. The proposed skew-asynchronous cellular automata update two consecutive cells chosen uniformly at random in each step. The present work focuses on elementary cellular automata, which are classified based on their dynamical behaviour under the proposed skewed environment. The dynamical behaviour of these cellular automata are compared with the fully-asynchronous cellular automata, which points out varieties of rich phenomenon under skewed environment. Some elementary cellular automata shift from convergence nature to divergence and some from non-convergence to convergence nature, if update style shifts from fully asynchronism to skewed asynchronism. We identify the cases where the divisibility of the lattice size by 2 or 4 introduces massive repercussion in the system following presence or absence of the atomicity property. Lastly, we theorize the reason behind convergence towards all 0 and all 1 point attractors under the proposed skewed environment which partially validates our experimental observations.