The ideas of fractals and fractal dimension are here translated into the realm of visual psychophysics. Borders between two fields of different luminance were used. Because of the finite grain of the visual system, fractal dimension need be defined only within a certain size range. For a fractal dimension of 1.15, the just-detectable difference in fractal dimension was found to be about 0.0085, rising to about 0.015 for a fractal dimension of 1.25. Reducing exposure duration from 1 s to 0.33 s decreases sensitivity to differences in fractal dimension, but there was no gain in increasing the exposure duration. Good visual observers who are naive to the task require some training before reaching optimal performance. The ability to discriminate fractal dimension differs between fractal edges of the same fractal dimension that were generated with differing statistical programs. Even after considerable training, an observer makes 29% errors when asked to distinguish a fractal edge generated with a Gaussian random walk from one with a rectangular random walk. Gaussian random walk fractals can be more easily distinguished from Poissonian and Cauchy ones.