Towards a Formal Understanding of Bateson’s Rule: Chromatic Symmetry in Cyclic Boolean Networks and its Relationship to Organism Growth and Cell Differentiation
Yuri Cantor, Bilal Khan, and Kirk Dombrowski
There has been considerable prior research on the biological processes of morphogenesis and cellular differentiation, and the manner by which these processes give rise to symmetries in biological structures. Here we extend our previous work on thermal robustness and attractor density in cyclic formal Boolean dynamical systems, introducing a new form of spectral analysis on digital organisms at the cellular level. We interpret the phenomena of radial and bilateral symmetry in terms of spatial periodicities in the color sequences, as manifested by an organism while it orbits in its attractors. We provide new results on the influence of various organism properties on its emergent color symmetries—providing initial insights toward an eventual formal understanding of metamerism and Bateson’s Rule.
Keywords: Boolean networks, dynamical systems, chromatic, symmetry