Patterning and Self-Organization Beyond Turing: From Myxobacteria to Flatworms

Turing's idea that diffusion differences between chemical species can drive pattern formation and select wavelengths has been a central building block for the modeling of patterns arising in chemistry and biology, from simple tabletop chemistry such as the CIMA reaction to morphogenesis and the formation of presomites. I will report on two studies of pattern formation that invoke pattern selection mechanisms quite different from Turing's. In the first example, I will show how simple nonlinear run-and-tumble dynamics can reproduce complex functionality from equidistribution over rippling to fruiting body formation in myxobacteria colonies [arXiv:1805.11903,arXiv:1609.05741]. In the second example, I will describe simple models for the astounding ability of planarian flatworms to regenerate completely from small fragments of body tissue, preserving polarity (that is, position of head versus tail) in the recovery [arXiv:1908.04253].