The Tale of Three Triangles

This video develops a novel argument for why Sierpinski’s triangle, the Chaos Game, and Pascal’s triangle colored mod 2 all form the same shape. It's much longer than anything I've created before, and I'm so happy with how it turned out. This is also a submission for 3Blue1Brown’s Summer of Math Exposition competition (SOME1). If you enjoyed this, check out more of my work at https://truax.io/ Timestamps: 00:00 Prologue 05:12 Chapter I 08:24 Chapter II 10:51 Chapter III 15:25 Chapter IV 21:57 Chapter V 29:08 Epilogue Song credits: • Prologue: Mind by Home, Polar Bears by Stevia Sphere • Chapter I: Resonance by Home • Chapter II: Close by Foewi • Chapter III: A Light in the Dark by Henrik Johnson • Chapter IV: Chemical Burns by Home, Traffic by Foewi • Chapter V: Rolling Hills by Oval Music, Simple by Oval Music • Epilogue: Breakfast by potsu x lando • Credits: Musician by Porter Robinson Software used: Manim, Community Edition, to produce the animations themselves. Visit their website https://www.manim.community/ to learn how to use the software, see documentation, or contribute to make the project even better. Da Vinci Resolve to chain together raw footage and arrange it on screen.