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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: https://linesthatconnect.github.io/bl... The viral sorting algorithm video which first sparked my interest:    • 15 Sorting Algorithms in 6 Minutes   The animations in this video were created using Manim: https://www.manim.community/ Music credits: Fluidscape by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/... Night Music by Kevin Macleod river - Calm and Relaxing Piano Music by HarumachiMusic ... And a couple of my own songs: The Fog:   / the-fog   Heavy Head, Light Rain:   / heavy-head-light-rain   Thanks For Watching:   / 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