This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.
Usually by a method such as taking a triangle, dividing it into
3 sub-triangles, and perturbing the center point. This process is then
repeated on the sub-triangles. This results in a 2-d table of heights,
which can then be rendered as a 3-d image. This is referred to as
midpoint displacement. Two references are:
1. M. Ausloos, "Proc. R. Soc. Lond. A" 400 (1985), pp. 331-350.
2. H.O. Peitgen, D. Saupe, "The Science of Fractal Images",
Available online is an implementation of fractal Brownian motion (fBm)
such as described in "The Science of Fractal Images". Lucasfilm became
famous for its fractal landscape sequences in "Star Trek II: The Wrath
of Khan" the primary one being the "Genesis" planet transformation.
Pixar and Digital Productions are have produced fractal landscapes for
Fractal landscape information available online:
EECS News: Fall 1994: Building Fractal Planets by Ken Musgrave
Gforge and Landscapes (John Beale)
Java fractal landscapes :
Fractal landscapes (applet and sources) by Chris Thornborrow