Uploaded September 2024 | Updated September 2026, 2 weeks ago

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In this video, we show how to use a random process of iteratively applying five affine transformations in the real plane to generate a 5-rep-tile known as the Mandelbrot Quintet. What happens if you do something similar with different affine transformations?

Here is a bit longer version (without words): youtu.be/rLxx6b-oJGo

Check out these videos for related constructions:
youtube.com/shorts/dklWNdM9WSg
youtu.be/rLxx6b-oJGo
youtu.be/NBI_5GdvqUo

If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!

This animation was inspired by an article written by Lorelei Koss that appeared in the Proceedings of Bridges 2015: 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: jstor.org/stable/2691339

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

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