Hi all, this video is my entry for Summer of Math Exposition 3.
References:
Veritasium Video: th-cam.com/video/ovJcsL7vyrk/w-d-xo.htmlsi=WhhnFleCEU5JvHFN
3D Bifurcation Gif: github.com/jonnyhyman/Chaos
Logistic Map: mathworld.wolfram.com/LogisticMap.html
Feigenbaum Constant: th-cam.com/video/ETrYE4MdoLQ/w-d-xo.htmlsi=aeA_8nwURqALdr6C
mathworld.wolfram.com/FeigenbaumConstant.html
Further Reading on when the Feigenbaum Constant applies:
mathworld.wolfram.com/SchwarzianDerivative.html
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:
th-cam.com/video/TPYvmSMdDWQ/w-d-xo.html
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