About the robustness of 1d cellular automata revising their temporal entropy

Abstract

Complimentary to existing description methods of one-dimensional cellular automata dynamics the present study proposes a new ‘micro-historicizing’ approach inspired by Wolfram’s concept of temporal entropy and Kitano’s concept of robustness derived from biology: introducing ‘temporal sub-attractors’ the cell activity of specific automata settings can be typified in a novel way as kind of underlying phase space similar to a conditional heat map representing the activity of individual cells. The robustness of such a sub-phase space can be derived from two morphological trajectories: a robust sub-phase space can be expressed graphically as a sequence of temporal sub-attractor loops of rebalancing activity curves. Whereas a bifurcation of the sub-phase space with continuously diverging curves indicates a non-robust automaton configuration. Conceptually, the temporal sub-attractors bring a biological stress component into the physically inspired cellular automata models, which might not only be of help for modelling in biology, but also in material science and engineering science.