This was so beautifully presented it brought tears to my eyes. I have long understood the mechanism of complex numbers, the geometry, and the beauty of the connectedness of the ideas. In the early days I programmed my own Mandelbrot set generator, and I've given lectures on the mechanics. But I have never seen it so well explained and carrying out the idea into folding of space and construction of the Julia set by reversing the iterative process. This was filled many of the larger holes in my knowledge and has inspired me to take it further. Fantastic.
Awesome that waves can be thought of as moving by rotating. It makes me think that all motion could be an illusion, a consequence of observing the universe in a limited number of dimensions. How simple could the universe actually be? If we connect enough dots, could it turn out that all of existence is a single rotating point?
This made me very very happy.