Mimicking Cellular Automata with Machine Learning part5
- Strong stochastic stability of cellular automata(arXiv)
Author : : Hugo Marsan, Mathieu Sablik
Abstract : We define the notion of stochastic stability, already present in the literature in the context of smooth dynamical systems, for invariant measures of cellular automata perturbed by a random noise, and the notion of strongly stochastically stable cellular automaton. We study these notions on basic examples (nilpotent cellular automata, spreading symbols) using different methods inspired by those presented in \cite{MST19}. We then show that this notion of stability is not trivial by proving that a Turing machine cannot decide if a given invariant measure of a cellular automaton is stable under a uniform perturbation.
2.Self-Reproduction and Evolution in Cellular Automata: 25 Years after Evoloops (arXiv)
Author : Hiroki Sayama, Chrystopher L. Nehaniv
Abstract : The year of 2024 marks the 25th anniversary of the publication of evoloops, an evolutionary variant of Chris Langton’s self-reproducing loops which proved that Darwinian evolution of self-reproducing organisms by variation and natural selection is possible within deterministic cellular automata. Over the last few decades, this line of Artificial Life research has since undergone several important developments. Although it experienced a relative dormancy of activities for a while, the recent rise of interest in open-ended evolution and the success of continuous cellular automata models have brought researchers’ attention back to how to make spatio-temporal patterns self-reproduce and evolve within spatially distributed computational media. This article provides a review of the relevant literature on this topic over the past 25 years and highlights the major accomplishments made so far, the challenges being faced, and promising future research directions.
