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

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. (C) 2021 Elsevier B.V. All rights reserved.