Chaos Game finds the Mandelbrot Quintet

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?

Check out these videos for related constructions:

#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:

[diribigal]

I just repeated this process 10000 times and, boy, are my arms tired.

[nemesisurvivorleon]

construction master : "you'll get use to it after 100 times"
kung fu master : "it takes 1000 times to master this move"
Weakest Mathematician : "only 10, 000 repetitions to finish this one math problem"

[johannesh]

When I learned about this general fact*, I was so hyped.
Fact*: Take any set of transformations that shorten lengths, like these here which differ only by a translation. (note that these don't have to come from matrices). Start with any (compact) set like the single point here. Apply all transformations to the set (taking the union of the images) to obtain the next set (here we picked only one point, but in general just take all points and apply all transfomations). The set will converge towards a set and this will in almost all cases be a fractal.
This way we can generate so, so many fractals, you can't even imagine.

[yassinees-sofyani]

Visualized it with js and html5 canvas it looks so cool, thanks for sharing

[gabrielbarrantes]

The question is, what is the deep relationship with the mandelbrod set?

[cyrangan]

I am convinced that there is a relationship between this pattern and the 3x+1 conjecture. I’m not one for mathematical proofs, but I think there’s some kind of crossover here.

[randominternetbro]

you and I have very different definitions of fun

[lf]

can also just apply transformation to every point generated by the last transformation instead of picking one at random

[erinmac]

This is mind-blowing! It makes me wonder if there's a relationship between these fractals and tesselation.... Other than that, this is beyond my current abilities. Super cool! 💜

[EvonixTheGreatest]

Is the random point pick important? If instead you apply the transform to every point then continue a few layers deep would it look different?

[aspirantsverse]

Which simulation software is used here ?

[CookieMage]

infinity stone ahh first transformation

[FarawayFragrance]

bro I keep getting these videos in my recommended, I’m not complaining, but I’m also not a mathematician

[Beaconism-Dollarism]

The font is too small. I canot see the transformations.

[Pyshgaming-vd]

introducing: the mandelbrot nonilionet

[SquaredNES]

Wouldn't it do the sane thing if you applied the transformation to ALL the points?

[enotikbteplovoze]

This shape might just failed art school 😂

[evilpandakillabzonattkoccu]

no, I don't think I can. That's cool though!!

[RUBINHO]

It is possible to construct this in geogebra?

[badabing]

how would you be able to derive the exact final shape without just doing this 10k times