Make a multitude of spirals, spinning. Since each spiral's arms will span the whole screen, spirals will overlap each other.
Spirals spiral outward at random logarithmic rates. Each spiral has a random color.

Make all spirals' origins at the center of the screen, or put them in random positions?

What to do at pixels where arms go over each other?
a) XOR them with eachother,
b) add them up
c) plot whichever one is designated to be 'on top'
d) make those pixels bright spots of an outstanding color? that way you see the patterns of their motions.

idea: if using method c, make it paradoxical in that one spiral can be 'on top' of another which is 'on top' of another which is 'on top' of the first spiral.

i've actually programmed this, but don't know if i have the source.