The reason generative art stopped looking like television static.
Plain random numbers are useless for organic form. Each one has nothing to do with its neighbour, so what you get is static.
Gradient noise fixes that by making nearby points produce nearby values. Ken Perlin wrote the first widely used version in 1983 while working on Tron, and later picked up a technical Oscar for it. Almost everything in generative art that reads as natural has some descendant of it underneath.
One layer of noise is smooth and rather dull. Add several at doubling frequency and halving amplitude, a trick borrowed from Mandelbrot and usually called fbm, and you get detail at every scale at once. Real terrain works the same way: mountains, then hills, then bumps underfoot. Three or four octaves is normally enough, and past about six you are paying for detail nobody can see.
Read the noise value at each point as an angle instead of a height and you have a vector field. Every point on the canvas now says go this way. Release particles into it, record where they went, and you get the long sweeping strands that define a whole genre of this work.
Curl noise, from a 2007 paper by Robert Bridson and colleagues, goes further. Taking the curl of the field makes it divergence-free, so nothing piles up and nothing thins out, and the result moves like a fluid rather than like a crowd walking downhill.
Perlin or simplex? Simplex is faster in higher dimensions and has fewer directional artefacts. In two dimensions, for art, you will struggle to tell them apart.
Why does my flow field look like hair? Because every particle is obeying the same field. Vary the step length, the lifetime, or where the particles start, and the uniformity breaks up.