Script to simulate the patterns on the zebrafish skin, based on the research of D. Bullara & al., 2015 [1]
The skin of zebrafish has characteristic patterns of stripes parallel to the anteroposterior axis that are found in all individuals; similar and yet not identical motifs. How is this pattern formed? Much research has been carried out on this subject, notably by the famous Alan Turing, who gave his name to the Turing bifurcation phenomenon at the origin of these patterns. However, although the widely accepted explanation is that Turing bifurcation involves diffusion, the paper that served as the starting point for this project calls this proposition into question. Indeed, based on the observations of Kondo & al's team that the chromatophores contained in the skin of zebrafish are activated and inhibited at short and long distances, Bullara & al. modeled an epidermis governed by these same interaction rules, ultimately demonstrating that the movement of pigment cells is not necessary for the generation of Turing patterns. It is this modeling which has been recoded in Python and then furthered in this project. Notably, different ways to code the boundaries (initially periodic) and two types of disturbances (a default and a cut). We can try to answer the following questions: how do the patterns react during disturbances? How to translate cell healing into modeling terms? Do the boundary conditions coding has an effect on the pattern?
[1] Bullara, D., De Decker, Y. Pigment cell movement is not required for generation of Turing patterns in zebrafish skin. Nat Commun 6, 6971 (2015). https://doi.org/10.1038/ncomms7971