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In this video, we explore the differences between starting with a random dot in a regular pentagon, octagon, and square and iterating the procedure of choosing a vertex (or midpoint for square) at random and moving a given distance from the current dot to the chosen vertex. In each case, the limiting set is fascinating.

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#chaos #chaosgame #pentagon #square #octagon #mathvideo​ #math​ #mtbos​ #manim​ #animation​ #theorem​​​ #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractals

For more videos related to the Chaos game from me, see
   • Chaos Game in a Hexagon  
   • Mandelbrot Quintet Fractal (a 5 rept...  
   • Twin Dragon Fractal (a 2 reptile): O...  
   • The Lévy Dragon from the Chaos Game (...  
   • Chaos game  Sierpinski triangle  
   • Shorts  
   • Shorts  

If you want to know more about the Chaos game, see the following links:
https://en.wikipedia.org/wiki/Chaos_game
https://mathworld.wolfram.com/ChaosGa...
https://math.bu.edu/DYSYS/chaosgame/...
   • Chaos Game  Numberphile  
   • Chaos Game | Fractals emerging from c...  

See more here (https://larryriddle.agnesscott.org/sy...) and on his website: https://larryriddle.agnesscott.org/if...

To learn more about animating with manim, check out:
https://manim.community
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Music in this video:
Behind The Sun by Vlad Gluschenko |   / vgl9  
Music promoted by https://www.freestockmusic.com
Creative Commons / Attribution 3.0 Unported License (CC BY 3.0)
https://creativecommons.org/licenses/...