Lyapunov’s Fractal (that Lyapunov knew nothing about) #SoME2
Hi everyone! I hope you enjoy my first video. I’ve known about Markus-Lyapunov Fractals for a few years now, and it surprised me that I couldn’t find any video explaining how they work - so I thought I’d take a stab at it myself! This is also my submission for Summer of Math Exposition 2.
Basic Lyapunov Fractal Demo in Shadertoy:
Further Reading:
A 1990 paper by Mario Markus that introduces the fractal:
Chapters:
0:00 Intro
1:00 Maps
3:20 The Logistic Map
5:44 The Bifurcation Diagram
7:29 The Lyapunov Exponent
11:35 Markus’s Modified Logistic Map
16:51 The Markus-Lyapunov Fractal
18:55 Overlapping Branches
20:37 3-D Bifurcation Diagram
23:18 3-D Lyapunov Fractals
23:59 Beyond the Logistic Map
Image credits:
Mario Markus picture:
Lyapunov picture:
Lyapunov picture (in thumbnail): :
2 years ago 00:24:42 1
