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.
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.
with the advantage that you can smoothly fold in reverse to find the set that doesn’t escape.
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.
I’m personally very glad you nevertheless decided to go ahead and publish this (pedagogically beautiful) essay; I’m already mentally drawing up a list of friends to share this with :)
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.
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.
I’m personally very glad you nevertheless decided to go ahead and publish this (pedagogically beautiful) essay; I’m already mentally drawing up a list of friends to share this with :)
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.