Noise and Intermediate Asynchronism in Cellular Automata with Sampling Compensation

Cellular Automata (CAs) are a class of discrete dynamical systems that are widely used to model complex systems in which the dynamics is specified locally at cell scale. In its classic definition, CAs performs with perfect synchronism. However, this does not stand for what happens at a microscopic level for physical and biological systems. Recent research has studied the CAs behavioral consequences of using intermediate levels of asynchronism, where only a fraction of the cells is updated at each time step. In this work we examine, in addition to intermediate asynchronism, the impact of different levels of noise, a perturbation that causes a cell to randomly change its state when it is updated. To conclude, we explore an observation mechanism in which sampling normalizes the updating differences introduced by asynchronism. Results show that this method reduces CAs behavior into two classes, chaotic and fixed-point. Explanations for observed behaviors are proposed.