Hi all, this video is my entry for Summer of Math Exposition 3.
References:
Veritasium Video: • This equation will change how you see...
3D Bifurcation Gif: https://github.com/jonnyhyman/Chaos
Logistic Map: https://mathworld.wolfram.com/Logisti...
Feigenbaum Constant: • The Feigenbaum Constant (4.669) Nu...
https://mathworld.wolfram.com/Feigenb...
Further Reading on when the Feigenbaum Constant applies:
https://mathworld.wolfram.com/Schwarz...
https://demonstrations.wolfram.com/Th...
Corrections: The tent map is x•min(x,1x), not x•min(x,x1)
Another great video exploring the relationship between the Mandelbrot Set & the logistic map:
• Relationship between Mandelbrot set &...
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