memeengine asked: re: the closeup of 100th roots of unity. Wouldn't that just be 4 boring points on the unit circle in the complex plane? What's with all the gradient-looking lines? Is there some context, or is this just a prettying up of 4 points? Thanks!
I can’t say for sure since that was all of the information I saw when I found the picture. I wondered the same thing though, and decided that it must be generated the way fractal images are: by iterating z^2 + c and mapping points that don’t go to infinity (converge or are periodic) in black (and using other colors to represent the speed of divergence), except in this case it is an iteration of
z^100 - 1
which would give the sequence 0, -1, 0, -1, … for roots of unity.
So the roots of unity would be periodic and so be black.
So I think this image shows how nicely points around the roots of unity behave with the function z^100 -1.
This is all just a guess though…