Twin Dragon Fractal (a 2 rep-tile): Order from Chaos (visual construction)

In this video, we show how to use a random process of iteratively applying two affine transformations in the real plane to generate a 2-rep-tile known as the Twin Dragon. What happens if you do something similar with different affine linear transformations?

Check out these videos for related constructions:
https://youtu.be/rLxx6b-oJGo
https://youtu.be/NBI_5GdvqUo

If you like this video, please check out my others and consider subscribing. Thanks!

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

This animation was inspired by an article written by Lorelei Koss that appeared in the Proceedings of Bridges 2015: https://archive.bridgesmathart.org/2015/bridges2015-423.pdf . 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

To learn more about animating with manim, check out:
https://manim.community

_________________________________________
Music in this video:
When The Lights Go On by Vlad Gluschenko | https://soundcloud.com/vgl9
Music promoted by https://www.free-stock-music.com
Creative Commons Attribution 3.0 Unported License
https://creativecommons.org/licenses/by/3.0/deed.en_US

Видео Twin Dragon Fractal (a 2 rep-tile): Order from Chaos (visual construction) канала Mathematical Visual Proofs