A complete description of the dynamics of legal outer-totalistic affine continuous cellular automata

Abstract This paper presents an investigation into the evolution and dynamics of the simplest generalization of binary cellular automata: Affine Continuous Cellular Automata (ACCAs), with [0,1] as state set and local rules that are affine in each variable. The focus lies on legal outer-totalistic ACCAs, an interesting class of dynamical systems that show some properties that do not occur in the binary case. A unique combination of computer simulations (sometimes quite advanced) and a panoply of analytical methods allow to lay bare the dynamics of each and every one of these cellular automata. The results show that in the class of ACCAs considered, one can observe all types of sensitivity: sensitivity to the change of the number of cells in the grid, sensitivity to slight changes in the parameters of a local rule and sensitivity to the change of a single value in an initial configuration.Mathematics Subject Classification (2020) MSC 37B15, MSC 68Q80