In my spare time in college, I enjoyed playing with sequences of image transformations. Start with a random grayscale image and convolve it with a Gaussian kernel ("blur" effect), treating the edges of the image as if they wrap around. Then apply a "folding" transformation like the logistic map x → 4x(1-x), familiar from chaos theory, to each pixel, so that black and white pixels become white, and gray pixels become black. If you keep alternating convolutions and folding, you will converge to a random pattern that looks somewhat like the stripes on a zebra. The width of the stripes is determined by the width of the Gaussian kernel. Because the individual transformations are rotation and translation invariant, so is the probability distribution over the resulting images.
I found it interesting to play with variations on this idea while aiming at a particular result. For example, how can we use symmetric transformations to generate a random pair of stripe patterns such that, when superimposed, the stripes of each image tend to intersect at right angles? How can we generate a visual analog of the Shepard scale auditory illusion, which sounds like an infinitely rising tone - in other words, how do we make a procession of random stripe images that seems to be continually shrinking? The below examples were all made in 2016.
