Chaos Game in Hexagon (bestagon?)

In this short, we show what happens when iterating the procedure of choosing a hexagon vertex at random and moving wo thirds the distance from the current dot to the chosen vertex.

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

If you want to know more about the Chaos game, see the following links:

To learn more about animating with manim, check out:

[jonathanlevy]

makes sense, those are the limits of all the sequences possible with 6 options for each value

[AA-iptp]

The shape in the center is known as Koch snowflake. It's such a great fractal

[JesseGilbride]

"Hexagons are the bestagons" ~ CGP Grey

(I have the tshirt 😛)

[muffinconsumer]

One thing I haven’t seen someone try is the chaos game in a non-regular polygon or a concave polygon. I assume it would just be butchered fractals

[youreoffline]

That's the reason why Hexagons Are The Bestagons

[fgvcosmic]

Works with triangles, too! Gives you a sierpinski triangle!

[NeroDefogger]

I love the sponge cube fractal and the pyramid fractal, I didn't know this one existed, I have an other fractal I love now

[jgsanchezm]

I think this perfectly exemplifies that random is different from chaos.

The “2/3” conditional is the key.

If the location of the second point on the line was also random, we definitely find chaos instead…

[bradenmiley]

I’m pretty sure that if you start with your first dot within some of the black parts of the hexagon, it’ll still make this shape it’ll just have the one outlier

[privateuser]

Amazing how chaos is so related to the generation of fractals 👏🏼👏🏼👏🏼😮

[mikaeloverfjord]

Had no idea that an infinite triangle fractal was connected to hexagons like this. 🤩

[ajeybakshi]

I like the fact that whenever he play a chaos game, he arrange the areas with colors

[snowyfox]

Hexagons within hexagons within even more hexagons...

[cheeseburgermonkey]

Feels like it has a connection to real numbers in base 6 or 6-adic numbers

[-petrichor-]

That's so cool! I would like to see someone do this in real life! 35, 000 can't be a lot right? Should take 35 mins.

[johnschwerdt]

A result that would not be obvious without a computer!!

[hareecionelson]

Another one is to start with 3 points of a triangle and move to the midpoint of lines connecting points to randomly selected vertices.

[abhishek]

Maths is beautiful even if I can't solve it ❤

[izzabelladogalini]

I've probably missed something obvious but if that pattern forms from all the dots how are some of them touching the sides of the hexagon, if each dot is ⅔ the distance to a random vertices from the previous dot then the previous dot would also have to be on a side line, as would it's previous dot etc

[Alsoknownasnerd]

Now try it while playing super hexagon.