From mazes to pulsating spots in the Gray-Scott model on the sphere скачать в хорошем качестве

From mazes to pulsating spots in the Gray-Scott model on the sphere

This simulation of the Gray-Scott model on the sphere uses a feed rate changing over time, which leads to patterns starting with mazes, which turn into pulsating spots, before reaching a uniform stable state. The Gray-Scott model 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 varies here from 0.045 to 0.015, while the kill rate b is constant 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: 3D view: 0:00 2D view: 1:01 The color hue and the radial coordinate in the first part depend on the concentration of type A. In part 1, the observer turns around the sphere on a circular orbit, centered at the center of the sphere. Part 2 uses a projection in equirectangular coordinates, which means that the x-coordinate is proportional to longitude, while the y-coordinate is proportional to latitude. 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 - 1 hour 53 minutes Part 2 - 1 hour 52 minutes Color scheme: Turbo, by Anton Mikhailov https://gist.github.com/mikhailov-wor... Music: "The Journey Ahead" by Ezra Lipp‪@Ezralipp‬ 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...