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Balancing Games
evin20

Despite the randomness, bridge is an excellent example, as "people who are serious about it" play duplicate bridge. Duplicate poker exists, but doesn't seem as popular.

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An Introduction To The Mandelbrot Set That Doesn't Mention Complex Numbers
evin*10

With Julia, step 3 is all dancers moving in the same direction in unison. This is a smooth non-intersecting movement just like the inverted steps one and two. With Mandelbrot, the dancers will move somewhat chaotically in step 3, inevitably colliding.

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An Introduction To The Mandelbrot Set That Doesn't Mention Complex Numbers
evin*70

For a wonderful visualization of complex math, see https://acko.net/blog/how-to-fold-a-julia-fractal/

This link primarily focuses on the related Julia fractal instead of the Mandelbrot as done here, with the advantage that you can smoothly fold in reverse to find the set that doesn't escape.

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3Yitz
This is a great read!! I actually stumbled across it halfway through writing this article, and kind of considered giving up at that point, since he already explained things so well. Ended up deciding it was worth publishing my own take as well, since the concept might click differently with different people. You can actually do this with the Mandelbrot Waltz as well! Of course you still need to know each point's starting position in order to subtract that for Step 3, but assuming you know that, you can do exactly the same thing, I believe.