2025/08/31 by Nassima Ait Sadi, Sadi, Nassima Ait, Rezki Chemlal +1
Computer Science · Materials Science · #Cellular Automata and Applications #Neural Networks Stability and Synchronization #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2509.00933
Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both topological and ergodic point of view. The main results of the paper show the impossibility for a cellular automaton with a fully blocking pattern to have a measurable irrational eigenvalues. Further more, a cellular automaton with a set of equicontinuity points of positive measure cannot have a measurable irrational eigenvalue.