Time-slice representation of space-time chaos in the Gray-Scott model

This is a variant of the video https://youtu.be/_C-7agqfmw4 showing "time-slices" of an evolution of the Gray-Scott model, in the sense that the z-coordinate depends on the time when the concentration of the first species exceeds a fixed threshold.
The Gray-Scott equation models the chemical reaction 2A + B → 3A, meaning that if two molecules of type A encounter a molecule of type B, the type B molecule is transformed into type A. In addition, type B molecules are produced at rate a (the feed rate), and type A molecules are transformed into an inert species at rate b (the kill rate).
For a large number of molecules, the system is described by the system of reaction-diffusion equations
d_t u = Delta(u) + u²v - (a+b)u
d_t v = D*Delta(v) - u²v + a(1-v)
where u and v describe respectively the concentrations of type A and type B molecules, Delta denotes the Laplace operator, and D measures the diffusion of type B molecules. The feed rate a is here equal to 0.026, while the kill rate b is equal to 0.051. The initial state is an elliptical region with only type A, surrounded by a sea with only type B.
The video has two parts, showing the same simulation with two different representation:
Concentration of A: 0:00
Threshold time: 1:12
In both parts, the z-coordinate depends on the first time the concentration of type A exceeds a fixed threshold. This quantity also determines the color in Part 2, while in Part 1, the color hue depends on the concentration of type A. The boundary conditions are periodic. The observer turns around the rectangular simulation region at constant altitude.

This simulation is inspired by the online simulator
https://visualpde.com/sim/?preset=GrayScott
that allows you to explore the effect of the different parameters on the system.

Render time: 1 hour 16 minutes
Color scheme: Turbo, by Anton Mikhailov
https://gist.github.com/mikhailov-work/6a308c20e494d9e0ccc29036b28faa7a

Music: "Burner" by Gunnar Olsen

See also https://images.math.cnrs.fr/Des-ondes-dans-mon-billard-partie-I.html for more explanations (in French) on a few previous simulations of wave equations.

#reaction_diffusion #Gray_Scott

The simulation solves a partial differential equation by discretization.
C code: https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html

Видео Time-slice representation of space-time chaos in the Gray-Scott model канала Nils Berglund