In the present paper we analyse the morphology of dendrites of cerebel
lar Purkinje cells and axon terminals in the cerebral cortex of rats.
We find that these three-dimensional biostructures are fractal over at
least one decade of length scales, with fractal dimension 1.68 +/- 0.
08 for the Purkinje cells and 1.28 +/- 0.17 for the axon terminals. We
also discuss the largelly unknown mechanisms underlying neurite outgr
owth which frequently develops neuronal shapes with fractal dimensions
very different from that predicted for diffusion-limited-aggregation
model (DLA) in three dimensions.