reaction_diffusion_systems
Reaction-diffusion systems can model many natural pattern-forming processes.
One very popular reaction-diffusion system is the Gray-Scott model, which consists of 2 coupled partial differential equations: $$ \frac{\partial u}{\partial t} = r_u \nabla^2 u - u v ^2 + f(1- u) $$ $$ \frac{\partial v}{\partial t} = r_v \nabla^2 v + u v ^2 - (f + k) v $$
In this model the interaction $u$ and $v$ can be seen as 2 chemicals each with their respective diffusion rates. $u$ and $v$ are simply two functions over some space (a 2D space in my case). $f, k$ are system-specific. We can think of $u$ and $v$ as two densities values distributed over a domain. In my case this domain is a 2-dimensional area. Which means that $u$ and $v$ are simply 2 textures.
This animation was made with python using numpy and scipy. A version of the python-script can be found here.
see also: