Reaction-diffusion equations can be utilized in order to describe processes of non-chemical systems as well as those containing one or more chemical substances that exhibit vast spatiotemporal patterns such as socioeconomic interactions, neutron diffusion, and biochemical reactions. Solutions to these equations can exhibit wave-like behavior as first described by Alan Turing in his 1952 article The Chemical Basis of Morphogenesis. Here, we explore the Gray-Scott and FitzHugh–Nagumo models in order to simulate the diversity of patterns found among species as observed on the skin, scales, and fur of animals and across the domains of life.

We leverage Flask to provide a web app with as an interface to modify the variables of reaction-diffusion equations to produce a GIF of the corresponding biological pattern such as the following zebrafish simulation:

The zebrafish pattern can be produced by using the interface with the parameters depicted below.

• Ryan Senoune
• Austin J. Szuminsky
• Yuliya Shpunarska
• Xavier L'Heureux

BSD 3-Clause License