Video

This is the 1800th video published on this channel (not counting a handful of videos I published multiple times due to compression issues). Once again, I thank you all for following and commenting, which motivates me to keep this channel going.
For any milestone video, I try to make something a little special. In this case, we have a first simulation of a new system that was on my to-do list for a long time, the Gray-Scott model. This system 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 0.037, while the kill rate b is equal to 0.06. 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:
2D view: 0:00
3D view: 1:21
The color hue and the z-coordinate in the second part depend on the concentration of type A. The boundary conditions are periodic. In part 2, the observer turns around the rectangular simulation region at constant altitude.

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

Render time: Part 1 - 47 minutes 20 seconds
Part 2 - 1 hour 1 minute
Color scheme: Cividis by Jamie R. Nuñez, Christopher R. Anderton, Ryan S. Renslow
https://journals.plos.org/plosone/art...

Music: "Kayak" by The Grey Room/Density & Time‪@TheGreyRoom‬

See also https://images.math.cnrs.fr/Des-ondes... 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-orlea...
https://www.idpoisson.fr/berglund/sof...