Every symbol on this picture represents a different pigment cell in a fish skin pattern. We created this pattern using computer simulations of a mathematical model. 

Zebrafish have stripes on their skin, but some fish that evolved from zebrafish have spots like these. Whether fish have spots or stripes, their patterns form because brightly-colored cells move around and organize themselves into a pattern. Think of these cells like birds interacting to form a flock in the sky -- they follow rules of behavior to make beautiful patterns.

With mathematical modeling and simulations, we search for the rules of behavior that pigment cells follow to create zebrafish stripes. When we change these rules in our model, different patterns form, like the spots in the picture. This shows one way that mathematics is used to study the evolution of skin pattern diversity in nature.

Alexandria Volkening 

NSF-Simons Center for Quantitative Biology 

Tools & Techniques: Computer simulations of a mathematical model