Unveiling the Hidden Connection Between the Logistic Map and the Mandelbrot Set 🔍

Hi all, this video is my entry for Summer of Math Exposition 3.

References:
Veritasium Video: https://youtu.be/ovJcsL7vyrk?si=WhhnFleCEU5JvHFN
3D Bifurcation Gif: https://github.com/jonnyhyman/Chaos
Logistic Map: https://mathworld.wolfram.com/LogisticMap.html
Feigenbaum Constant: https://youtu.be/ETrYE4MdoLQ?si=aeA_8nwURqALdr6C
https://mathworld.wolfram.com/FeigenbaumConstant.html

Further Reading on when the Feigenbaum Constant applies:
https://mathworld.wolfram.com/SchwarzianDerivative.html
https://demonstrations.wolfram.com/TheSchwarzianDerivativeOfIteratedFunctions/

Corrections: The tent map is x•min(x,1-x), not x•min(x,x-1)

Another great video exploring the relationship between the Mandelbrot Set & the logistic map:
https://youtu.be/TPYvmSMdDWQ

Chapters:
0:00 Intro
00:31 Bifurcation Diagram
02:20 Mandelbrot Set
04:52 3D Bifurcation Gif
05:14 Building a 3D Bifurcation Diagram
07:48 Recap
08:45 Logistic Map Fractal
09:32 Logistic Map 3D Bifurcation Diagram
10:09 Feigenbaum Constant
12:00 Outro