Let's say we have a function f_{c}(z) = z^{2} + c, where c and z are complex numbers. For this, we start with some complex number, say i + 1, and z = 0. Spoiler alert: f_{i + 1}(0) is i + 1 (shocker, I know). We then input this answer for z, getting 3i + 1. Let's say I keep iterating this forever. Does it converge or diverge? This comes out to be false, but are there any? Yes, and these are all parts of the Mandelbrot Set. It looks like this:

This definitely is beautiful, but what if c was constant for all values, and z was our complex value, then we iterated and see which converged? This is called a Julia set, and it is just as beautiful. Code here. Here's what it looks like:

That one guy that's always on

I want to be able to insert and run my processing code right there, but I can't upload my pde file to do it. How would you guys do it?

That one guy that's always on

@Ldhmachin may be able to help, drop him a direct message

If you send me the code as a message or link to GitHub, I'll review and upload it here if I can.

"Computer science is no more about computers than astronomy is about telescopes."

~ Edsger W. Dijkstra

The code is linked to in the post. You just uncomment all things regarding the angle variable, and in the for loops, add ca and cb instead of xco and yco.