2012/10/04 by Héctor Zenil, Zenil, Hector
Biochemistry, Genetics and Molecular Biology · Computer Science · #Cellular Automata and Applications #Cellular Automata and Lattice Gases (nlin.CG) #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Physical sciences #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.1210.1572
openalex publication_date 2012/10/04 · openalex created_date 2022/09/22 · openalex updated_date 2026/07/28
Despite having advanced a reaction-diffusion model of ODE's in his 1952 paper\non morphogenesis, reflecting his interest in mathematical biology, Alan Turing\nhas never been considered to have approached a definition of Cellular Automata.\nHowever, his treatment of morphogenesis, and in particular a difficulty he\nidentified relating to the uneven distribution of certain forms as a result of\nsymmetry breaking, are key to connecting his theory of universal computation\nwith his theory of biological pattern formation. Making such a connection would\nnot overcome the particular difficulty that Turing was concerned about, which\nhas in any case been resolved in biology. But instead the approach developed\nhere captures Turing's initial concern and provides a low-level solution to a\nmore general question by way of the concept of algorithmic probability, thus\nbridging two of his most important contributions to science: Turing pattern\nformation and universal computation. I will provide experimental results of\none-dimensional patterns using this approach, with no loss of generality to a\nn-dimensional pattern generalisation.\n