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If you repeatedly apply one of three simple functions picked at random you might end up with Sierpinski triangle.

This sounds fascinating! I know what a Sierpiński triangle triangle is but I'm having so me trouble seeing the connection from picking functions randomly to the triangle. Is there some graphics or animation somewhere on the web that someone can point me to visualize this better?

You can read section Chaos Game here:

https://en.m.wikipedia.org/wiki/Sierpi%C5%84ski_triangle

It basically using the fact that fractal is self similar. So picking one function (that scales whole triangle to one of the one thirds) and transforming single point on a fractal into a new point also gets you a point on the fractal.

If you repeat this process many times you get a lot of points of the fractal.

You can even start the process at any point and it will "get attracted" to the fractal.

That's why fractals are called strange attractors.

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