Chaos, fractals and dynamics: computer experiments in mathematics (R. Devaney; Amer. Math. Soc, 1989; one hour). Iteration in one and two dimensions, Julia sets for sin, cos and exp functions. Clear explainations and nice pictures.
Transition to chaos (R. Devaney; Science Television, 1990; 65 minutes) Iteration, cobwebs, Sarkovskii's theorem, the Feigenbaum diagram, Julia sets and the Mandelbrot set. A nice lecture, like the previous video.
The beauty and complexity of the Mandelbrot set ("University Edition"; J. Hubbard, Amer. Math. Soc., 1989; 73 min). Iteration including Newton's method, the Mandelbrot set, equipotential lines for the latter.
Lindenmayer systems and space-filling music (Stephanie Mason, The Geometry Center, University of Minnesota; 1992) A short video which puts "space-filling" music to space-filling curves.
Mandelbrot sets and Julia sets (Art Matrix; 1990; two hours) Movies of spectacular zooms into and around the Mandelbrot and Julia sets made with a supercomputer. Unfortunately no documentation is available as to where we are at a given moment (?).