a julia set fractal can be created with repeated twistings and translations of a starting image. The twistings double the detail in the picture, and correspond to complex square-roots pic.twitter.com/M9XhWElehp
I discovered this way of growing the Mandelbrot set. The repeated operation helps me understand where the Mandelbrot set gets its shape and detail pic.twitter.com/f3FiYGgHyj
It is convenient to know a few small Pythagorean triples for when you need an arbitrary rotation matrix, so you can fill it up without resorting to sines and cosines. pic.twitter.com/DJyXVMSPWj