Reaction-diffusion system

The image was produced by forming a texture on the walls of a tunnel using a reaction-diffusion equation.

The system used was proposed by Alan Turing, as a model for the formation of coloured patterns on the skin of animals. It consists of a complicated system of nonlinear partial differential equations.

The system is simulated here by dividing 2-dimensional space up into a grid. At each point on the grid two quantities are stored, each representing the concentration of a particular chemical. The concentration at each point is affected by the other points nearby.

The concentrations affect each other in two ways: firstly, the chemicals tend to diffuse (in other words, they tend to move from places where there is a high concentration to places where there is a low concentration); secondly, they also react with each other. It is this second interaction (the reaction part) that is nonlinear and can result in the complex patterns that emerge.

In order to simulate an infinite grid, we connect the top and bottom rows and the left and right columns of the grid together.