Reaction Diffusion

First steps in R&D

It’s all about research … and a bit about development. When the two efforts come together, they form the well known acronym R&D.

However in this instance, it is hijacked for a greater purpose, known as Reaction-Diffusion, a mathematical model well know in chemistry in biology.

Two important scientific fields, but also two preferred playgrounds for sexual animal species: Male and female primeval attraction heavily relies on biological differences and hormonal chemistry. Their interaction results in a complex web of innumerable diffuse chain reactions, eventually resulting in the generation of a new being.

For this reason, I chose as a seed image the Chinese ideograms for man and Woman, and ran a few lines of Gray-Scott algorithm over it, to produce the below animation.

(Note: The AnimUtils extension to the ToxicLibs library used here is unfortunately not yet available in Javascript for execution in a browser)

Reaction Diffusion

According to Wikipedia:

Reaction–diffusion systems are mathematical models which explain how the concentration of one or more substances distributed in space changes under the influence of two processes: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space.

Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics and ecology. Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential equations. They can be represented in the general form

\partial_t \boldsymbol{q} = \underline{\underline{\boldsymbol{D}}} \,\nabla^2 \boldsymbol{q} + \boldsymbol{R}(\boldsymbol{q}),

where each component of the vector q(xt) represents the concentration of one substance, D is a diagonal matrix of diffusion coefficients, and R accounts for all local reactions. The solutions of reaction–diffusion equations display a wide range of behaviours, including the formation of travelling waves and wave-like phenomena as well as other self-organized patterns like stripes, hexagons or more intricate structure like dissipative solitons.

According to

The Gray-Scott reaction diffusion model is a member of a whole variety of RD systems, popular largely due to its ability to produce a very varied number of biological looking (and behaving) patterns, both static and constantly changing. Some patterns are reminiscent of cell devision, gastrulation or the formation of spots & stripes on furry animals.

As with all RD models, these patterns are the result of an iterative process evaluating each cell of the simulation space based on the concentrations of the two main parameters (for Gray-Scott usually named f and K) of the reaction equation as well as taking into account the concentrations of these 2 substances in neighboring cells.

Technologies: Processing 2, with the ToxibLibs library

Features: Reaction-Diffusion implementation on a bitmap seed.


Leave a Reply