Multifractal properties of R90 cellular automaton with memory
Standard Cellular Automata (CA) are ahistoric (memoryless Markov process), i.e., the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article considers the fractal and multifractal properties of an extension to the standard framework of CA implemented by the inclusion of memory capabilities. Thus, in CA with memory, while the update rules of the CA remain unaltered, historic memory of all past iterations is retained by featuring each cell by a summary of all its past states. A study is made of the effect of historic memory on the multifractal dynamical characteristics of one-dimensional cellular automata operating under one of the most studied rules, rule 90, which is well known to display a rich complex behavior.
multifractal properties memory cellular automata scaling exponents