Methods of digital image analysis have been adapted to measure the fractal dimension of cellular profiles. The fractal dimension is suggested as a useful measure of the complexity of a contour. Three methods produce similar results when applied to constructed, near-ideal fractal figures. Comparison of the measurements for a variety of image types indicates the measurement accuracy in each case and may help in interpreting the results when applied to real, non-ideal cell images of unknown fractal dimension. Two of the methods are currently adopted as appropriate for use on neuronal contours. A correlation exists between the complexity of these contours and the magnitude of the estimated fractal dimension.