Chaos Game: From Random Dots to the Sierpinski Triangle

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[00:00:00]Three rules.

[00:00:02]Can they create a perfect shape?

[00:00:04]Pick a random corner.

[00:00:06]Move halfway. [music] Repeat.

[00:00:10]At first, pure noise.

[00:00:13]But after thousands of jumps, a perfect fractal triangle.

[00:00:23]But why?

[00:00:25]Look at any corner.

[00:00:28]Three copies.

[00:00:30]Each one half the size.

[00:00:33]This is the only shape unchanged by all three rules.