Spots to stripes: using machine learning to navigate pattern formation space

Current models of pattern formation (e.g., Turing reaction-diffusion theory) can generate many observed animal pigmentation patterns. However, their dependence on many interacting parameters makes it difficult to explore their full phase space of patterns. This is an important problem because research in cell signaling and developmental biology allows us to generate increasingly accurate pattern formation models. In this study, we first defined a “measure space” using 25 different measures of pattern geometry (e.g., feature circularity, compactness, intensity variance). We mapped photographs of pigment patterns in measure space and classified them using k-means clustering. We found that three measures were sufficient to group patterns into distinct classes (e.g., spots, stripes, labyrinthine, etc.) The next phase involves using this measure space as a guide for navigating the complex parameter space of a new pattern formation theory. For example, all known patterns generated by the model and a new test pattern (for which the model parameterization is unknown) first are mapped onto measure space. To determine the parameters needed to form the test pattern, a guided search can be performed in parameter space using the measure space distance between the test and known patterns.