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 resulting image distribution.

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.