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  • 2 года назадОпубликованоPhysics for the Birds

Turings Cake (and other wrinkly math)

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... Become a Patreon member: 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Patterns in Nature 2:15 Simulating Reaction-Diffusion 4:50 Cake Game Plan 6:29 Why are wrinkles wrinkly? 9:53 Turing's Unpublished Work 11:26 Conclusion Thank you to Caleb Birtwistle for captioning!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: Reaction-Diffusion in nature: Mbu Pufferfish: Simulating Reaction-Diffusion: Gray-Scott Model: Zebrafish Patterns: Tiger Skin Cake Recipe: Why fingers wrinkle: Math of wrinkles: Math of wrinkly spheres: ~dunkel/Papers/ Turing-Swift-Hohenberg EQ: Turing's unpublished notes: Patterns in paint blog: