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This article outlines the main ideas of the demonstrations of a proof of Claim I and Claim II, which can be obtained by results in the paper and by a simple construction from dynamical systems theory. Additionally, Supplementary Material (SM) considers two-component reaction-diffusion systems with spatial inhomogeneities, which can simulate the known Rössler system exhibiting chaotic behavior. The article also discusses the use of a binary tree for cell differentiation in organisms consisting of 4 cell types, and a layered one-dimensional (1D) pattern consisting of cells of two types, red and blue.
