The Bubble Sort Curve

A derivation of the curve that is approximated by a common visualization of the bubble sort diagram. Read the full proof on my site: The viral sorting algorithm video which first sparked my interest: The animations in this video were created using Manim: Music credits: Fluidscape by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. Night Music by Kevin Macleod river - Calm and Relaxing Piano Music by HarumachiMusic ... And a couple of my own songs: The Fog: Heavy Head, Light Rain: Thanks For Watching: Chapters: 00:00 Intro: 0:37 Laying the Background 3:20 How Bubble Sort Works 6:59 Mathematically Describing Diagrams 9:13 Stretching the Diagrams 11:52 Visual Derivation 14:38 Symbolic Derivation 16:48 Nice! 17:07 A Rigorous Solution