Fractal patterns for dendrites and axon terminals

In the present paper we analyse the morphology of dendrites of cerebellar 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 outgrowth which frequently develops neuronal shapes with fractal dimensions very different from that predicted for diffusion-limited-aggregation model (DLA) in three dimensions.