A three-dimensional image generator generates a random signal which it filters in two dimensions generate a realistic three-dimensional image of a natural object such as ocean waves or clouds. By performing the filtering operation repeatedly on overlapping intervals of the random signal, related images can be obtained to generate moving scenes at real-time rates. Two or more partial image generators can be connected in parallel to generate different directions of motion, or different parts of a complex scene. Within each partial image generator, two or more space filters can be connected in parallel to generate superimposed patterns, such as small ripples superimposed on large waves. This image generator is much faster than previous, fractal image generators.