2007/07/25 by Alexander D. Wissner‐Gross, Wissner-Gross, Alexander D.
Computer Science · Engineering · #Cellular Automata and Applications #Cellular Automata and Lattice Gases (nlin.CG) #Evolutionary Algorithms and Applications #FOS: Physical sciences #Modular Robots and Swarm Intelligence
paper · pdf · doi:10.48550/arxiv.0707.3657
openalex publication_date 2007/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Individual cellular automata rules are attractive models for a range of biological and physical self-assembling systems. While coexpression and coevolution are common in such systems, ensembles of cellular automata rules remain poorly understood. Here we report the first known analysis of the equally weighted ensemble of all elementary cellular automata (ECA) rules. Ensemble dynamics reveal persistent, localized, non-interacting patterns, rather than homogenization. The patterns are strongly correlated by velocity and have a quasi-linear dependence on initial conditions. Dispersion from a single initial site generates peaks traveling at low-denominator fractional velocities, some of which are not discernible in individual rules, suggesting collective excitation. Further analysis of the time-evolved rule space shows the 256 ECA rules can be represented by only approximately 111 principal components. These results suggest the rather surprising conclusion that rich self-assembly is possible without favoring particular local interactions.