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These visualizations are generated by iterating a function of complex numbers.

This function is iterated at every point in the complex plane from -2-2i to 2+2i

Imagine the function zn+1 = zn2 + c where Z0 = 1

At point 0+0i,

Clearly, this function will never diverge, so we color (0+0i) black

At point 0+i

The magnitude of z2 is 2, so we know this iteration will continue to diverge. We color it a different color since it took 2 iterations to diverge.

You can define simple functions of complex numbers using a simple stack machine notation

Expressions are compiled to GLSL and run inside a fragment shader on the GPU