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Is the Logistic Map hiding in the Mandelbrot Set? |

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Desdenova

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

posted by Halmich4v