Pattern formation by local self-enhancement and long range inhibition

Like other biological processes pattern formation is based on the interaction of molecules. In order to find a mathematical description for a particular process the concentrations of the substances involved must be described as a function of space and time. This is possible by using equations that describe the changes in concentration over a short time interval as a function of other substances. Adding these concentration changes to given initial concentrations provides us with the concentration at a somewhat later time. Repetition of such a calculation provides the total over the course of time. Three factors are expected to play a major role in the concentration change: the rate of production, the rate of removal (or decay), and the loss or gain due to an exchange with neighbouring cells, for instance by diffusion.