Tutorial: How to simulate reaction-diffusion equations

This video explains how to make the simulations of the heat equation and of reaction-diffusion equations found on this channel. It then discusses the physics or biology behind some of these simulations.
After making the video, I realized that the small inset showing me filmed by my laptop's camera freezes about 34 minutes into the video. Perhaps OBS studio was not able to handle the video streams of the simulations and the camera all at once. But I figured this is not really important for following the video, as the audio and the main presentation work all right.
Introduction: 0:00
Derivation of the heat equation: 1:25
Properties of the heat equation: 3:31
Simulating the heat equation in 1D: 13:02
Simulating the heat equation in 2D: 16:40
Reaction-diffusion equations: 22:05
The Allen-Cahn equation: 28:06
Rock-Paper-Scissors: 32:18
Rock-Paper-Scissors-Lizard-Spock: 35:56
The FitzHugh-Nagumo equations: 41:39
Simulations of the heat equation: • Heat equation
Simulations of reaction-diffusion equations: • Reaction-diffusion equ...
Heat equation with Mandelbrot boundary: • The Mandelbrot capacitor
Rock-Paper-Scissors equation: • Larger spirals in the ...
Heat equation with Mandelbrot boundary and field lines: • The Mandelbrot capacit...
1D Allen-Cahn equation: • Chain of particles in ...
2D Allen-Cahn equation: • The 2D Allen-Cahn equa... )
Rock-Paper-Scissors equation: • Colliding vortices in ... )
Symmetric Rock-Paper-Scissors-Lizard-Spock: • A Rock-Paper-Scissors-...
Asymmetric Rock-Paper-Scissors-Lizard-Spock: • Transition from 3-bran...
The FitzHugh-Nagumo equations: • Phase of spiral waves ...
Playlist with tutorials: • Tutorials
C code: github.com/nilsberglund-orlea...
www.idpoisson.fr/berglund/sof...
#simulation #reaction_diffusion #heat_equation #rock_paper_scissors #spiral

[@444haluk]

So stoked!

[@rotskep]

omg i was just searching for how to make this.

[@Prof.JuanCarlos.Barreto]

Excelent

[@NilsBerglund]

Thank you!

[@bakhshandehamin]

Why last one went of slower?

[@NilsBerglund]

I assume you refer to the 1D Allen-Cahn equation. The rightmost domain contains 6 points on the positive side, which are pulled towards +1, but two of these points are also pulled by their neighbors towards negative values. In the end, the second effect wins, but it takes some time. The other domains will also disappear, until the field is constant, equal to -1 or +1. But the larger a domain, the longer it takes for it to disappear.

[@bakhshandehamin]

@@NilsBerglund Indeed yes. Once again thank you so much for all your effort. I have learned a lot from you.

[@clown134]

oh snap does this have anything to do with my request for a tutorial on how to run the software on your github?

[@NilsBerglund]

Not yet, I'm afraid - but I may come to that later on.

[@Life_42]

37:15 I like this one :)

[@NilsBerglund]

Thanks!