Tutorial: How to simulate reaction-diffusion equations
Channel: Nils Berglund
Date: 2023-05-21

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: https://youtube.com/playlist?list=PLAZp3rbgWLo0JYHpmSzVePBIW9tA6v6y4
Simulations of reaction-diffusion equations: https://youtube.com/playlist?list=PLAZp3rbgWLo3X0WkOMfXgtKmhBxskOeWa
Heat equation with Mandelbrot boundary: https://youtu.be/8ygylNhf0n4
Rock-Paper-Scissors equation: https://youtu.be/TORwMc2AaRE
Heat equation with Mandelbrot boundary and field lines: https://youtu.be/Yr040XeN14c
1D Allen-Cahn equation: https://youtu.be/NDQHepkSeS8
2D Allen-Cahn equation:https://youtu.be/yX0EAxZHNCQ)
Rock-Paper-Scissors equation: https://youtu.be/QcxpZKWbLd4)
Symmetric Rock-Paper-Scissors-Lizard-Spock: https://youtu.be/-Qap_7skcIA
Asymmetric Rock-Paper-Scissors-Lizard-Spock:  https://youtu.be/cioB22z7A9A
The FitzHugh-Nagumo equations:  https://youtu.be/8hCSNkhzOmI
Playlist with tutorials: https://youtube.com/playlist?list=PLAZp3rbgWLo1ZKxqNzl04oaQhpbv_5mg9

C code: https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html

#simulation #reaction_diffusion #heat_equation #rock_paper_scissors #spiral