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.

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.

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.