Terdragon from the Chaos Game (visual fractal construction from iterated function system)
In this video, we show how to use a random process of iteratively applying three affine transformations in the real plane to generate a 3-rep-tile known as the Terragon. What happens if you do something similar with different affine linear transformations?
Check out these videos for related constructions:
• Mandelbrot Quintet Fractal (a 5 rep-t...
• Chaos Game in a Hexagon
• The Lévy Dragon from the Chaos Game (...
• Twin Dragon Fractal (a 2 rep-tile): O...
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This animation was inspired by articles written by Lorelei Koss, one that appeared in the Proceedings of Bridges 2015: https://archive.bridgesmathart.org/20...
and one that appeared in the September 2022 issue of Math Horizons:
https://doi.org/10.1080/10724117.2022...
For more information, you should also check out the related article "Fractal Tilings in the Plane" by Richard Darst, Judith Palagallo and Thomas Price from the February 1998 Mathematics Magazine: https://www.jstor.org/stable/2691339
Or you can check out Larry Riddle's fantastic site with lots about this fractal and others: https://larryriddle.agnesscott.org/if...
#chaos #chaosgame #terdragon #dragonfractal #mathvideo #math #mtbos #manim #animation #theorem #iteachmath #mathematics #dynamicalsystems #iteratedfunctionsystem #dynamics #fractals
To learn more about animating with manim, check out:
https://manim.community
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Music in this video:
The Sun Will Rise by Vlad Gluschenko | / vgl9
Music promoted by https://www.free-stock-music.com
Creative Commons / Attribution 3.0 Unported License (CC BY 3.0)
https://creativecommons.org/licenses/...
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