Cellular automata analysis of life as a complex physical system - Tropp,Simon (2020)
This thesis regards the study of cellular automata, with an outlook on biological systems. Cellular automata are non-linear discrete mathematical models that are based on simple rules defining the evolution of a cell, depending on its neighborhood. Cellular automata show surprisingly complex behavior, hence these models are used to simulate complex systems where spacial extension and non-linear relations are important, such as in a system of living organisms. In this thesis, the scale invariance of cellular automata is studied in relation to the physical concept of self-organized criticality. The obtained power laws are then used to calculate the entropy of such systems and thereby demonstrate their tendency to increase the entropy, with the intention to increase the number of possible future available states. This finding is in agreement with a new definition of entropic relations called causal entropy.
Keywords: Cellular Automata; Self-organized Criticality; Casual Entropy; Entropy Maximization; Causal Entropic Forces; Biological Systems; Life; Game of Life; Statistical Physics; Non-linear Models