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Although there is a growing interest in the application of fractal analysis in neurobiology, questions about the methodology have restricted its wider application. In this report we discuss some of the underlying principles for fractal analysis. we propose the cumulative-mass method as a standard method and we extend the applicability of fractal analysis to both 2 and 3 dimensions. We have examined the relationship between the method of log-log Sholl analysis and fractal analysis and have found that they correlate well. Measurements of physiologically characterized retinal ganglion cells indicate that different cell types can have significantly different fractal dimensions. Such differences may allow the correlation of the physiological type of a neuron with its morphological fractal dimension.

We show that-over a range of length scales r-the shapes of quasi-two-dimensional retinal neurons are fractal objects, and hence may be quantitatively characterized in part by their fractal dimension d/.We analyze the shapes of numerous retinal neurons, both in vivo and in vitro. The neurons in vivo are found to have a fractal dimension df of 1.68 ±0.15. We also propose an explanation of certain stages of neuronal shape development in terms of a diffusion-limited-aggregation model, which predicts

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