Turing's Cake: Uncovering the Math Behind Its Intricate Patterns 🧁

Tiger skin cake is named after its intricate striped patterns, but they might be more than just decoration. I have a hunch that this cake is an example of a Turing pattern, the same mathematical model that gives a pufferfish its spots and your brains its wrinkles. We'll learn about Turing patterns and how to simulate them, mathematical models for wrinkling surfaces, and the Swift-Hohenberg equation that was first used to describe convection -- or, at least that's how we thought it was first discovered...

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0:00 Intro
0:38 Patterns in Nature
2:15 Simulating Reaction-Diffusion
4:50 Cake Game Plan
6:29 Why are wrinkles wrinkly?
9:53 Turing's Unpublished Work
11:26 Conclusion

Thank you to Caleb Birtwistle for captioning!

Turing's paper: https://www.dna.caltech.edu/courses/cs191/paperscs191/turing.pdf
Reaction-Diffusion in nature: https://www.science.org/doi/10.1126/science.1179047
Mbu Pufferfish: https://www.youtube.com/watch?v=T83pQ825-Bs
Simulating Reaction-Diffusion: https://www.karlsims.com/rd.html
Gray-Scott Model: https://groups.csail.mit.edu/mac/projects/amorphous/GrayScott/
Zebrafish Patterns: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2689028/
Tiger Skin Cake Recipe: https://www.youtube.com/watch?v=Ich__KlBnWs
Why fingers wrinkle: https://royalsocietypublishing.org/doi/10.1098/rsbl.2012.0999
Math of wrinkles: https://www.sciencedirect.com/science/article/abs/pii/S0022509608000380
Math of wrinkly spheres: https://math.mit.edu/~dunkel/Papers/2015StEtAl_NatMat.pdf
Turing-Swift-Hohenberg EQ: https://www.researchgate.net/publication/347410560_Labyrinthine_patterns_transitions
Turing's unpublished notes: https://www.sciencedirect.com/science/article/pii/S0315086015000397
Patterns in paint blog: http://www.pforbes.org/blog/turing-patternms-in-paint