texturesynthesis

The reaction-diffusion paradigm is a mathematical model which tries to model and generate patterns that are found in nature. In this model two or more chemicals diffuse over a certain region and react together to form patterns which hresemble naturally occuring ones. The first such model was proposed by Alan Turing in 1952. Reaction-diffusion can produce a variety of spot and stripe patterns, much like those found on many animals. Developmental biologists think that some of the patterns found in nature may be the result of reaction-diffusion processes. Reaction-diffusion models are also sometimes used in population simulations and in epidemiology.

The idea is that certain cell properties (such as generation of pigments) are determined in the embryo based on the local concentration of one or more chemicals referred to as morphogens. The concentrations of the morphogens are determined by two concurrent processes: diffusion (spreading of a chemical through the tissue) and reaction (chemical reaction in which morphogens can be created or destroyed, based on their concentrations in each cell). Such a mechanism is called a reaction-diffusion system.

Mathematically, such systems are modeled as a system of non-linear partial differential equations. Such equations have no closed form solutions in the general case, but they can be solved approximately using a numerical technique referred to as finite differences.

In this project we have implemented two reaction-diffusion systems - a two chemical system described by Turing in 1952 to produce spots, and a five-chemical system described by Meinhardt which produces striped patterns. In addition, we have also experimented with various choices of the parameters in order to produce complex textures.

Displayed below are some of the textures that we have developed using the system that we made.