Traditional computer graphics modeling techniques have failed to capture the complexity of natural topography. Solutions to this problem have been found by using fractal geometry. This paper provides an introduction to fractal geometry, including fractal algorithms, dimension, and self-similarity. Two distinct categories of fractals, deterministic and random, are compared. The random fractal, and in particular, the 1/f-noise model of fractional Brownian motion (fBm), simulates natural terrain. Three different methods of synthesizing fBm are investigated: midpoint displacement, random faults, and Fourier analysis. Images of synthesized topography are presented to aid in visualizing the algorithmic steps and final results of each procedure. The attributes of each method are explained, and suggestions for applying the techniques to particular rendering problems are given.