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.