Chaos game - Sierpinski triangle

In this short, we play the chaos game using randomness to find order and create the Sierpinski triangle. Can you explain why this works?

#math #manim #fractal #fractal #sierpinski #chaosgame #chaos #mathshort #visualmath

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Music in this short (a 10 second cut):
Creative Commons Attribution 3.0 Unported License

[villeskarin]

I’ve always wondered what happens if you start in the middle, pretty cool though

[B-ke]

I love fractals! It's like an infinitely looped video. This is a really cool way to create one!

[xpm]

you can also just get rid of the middle section for each iteration

[robinbrowne]

That is one of the weirdest mathematical things
🙂👍

[LengLy-xb]

Its... Its... A​ MASTERPIECE!! But when i flip it upside down it kinda looks like your you tube logo so that means your logo is made buy the sierpinski triangle

[dAni-ikhv]

i REALLY want to make this in Desmos...

[dudefromcav]

not really chaotic if the rule is very restrictive, 1 the area is inside the triangle so it's not really random, 2 it's always half the distance of the dots inside of same triangle, you're bound to get triangle patterns eventually

[mrbrown]

Your random selection is the same
respective sequence used in the square
example.

[cloverisfan]

Why can placing dots in a triangle yield the Zelda logo?

[pritampal]

thanks, today I did it on fortran and gnuplot 🤷🏻‍♂️

[yusufdenli]

That was fantastic, but why??
can you proof this?

[randomsircle]

Can we animate long division in Manim ? If we could do you know any tutorial or document for the same ?

[AkamiChannel]

What if you also allow the midpoints of the edges of the triangle? What do you get then?

[Oberatous-Udurabas]

What if your first dot is in the center of the triangle

[stephengibbons]

I did a Computer Science project at age 17, for which I chose to do fractal generation.

I looked at the generalisations of this method (and of taking Pascal's Triangle modulo 2), and discovered that if you start with a hexagon, and use ⅔ rather than ½, you get a fractal made up of the Koch Snowflake fractal, and if you start with a 3x3 square lattice of points with the middle one removed, and also use ⅔, you then get the Sierpinski Carpet


Edit: Just found your video about the hexagon case.

[curiosidadesdemariaemilia]

What happens if you pick a point that's not the middle?

[derekthompson]

Does it also draw the original triangle's edges? Can't find a video that doesn't show the border but I have to know: how can a point ever appear along the original edges?!

[AdielXD]

What if we place points outside the triangle?

[u_judgement]

Lets play the chaos game.

If your health drops to 0, you will lose

[gregjacksun]

What happens if you start at the centroid of the equilateral triangle?