Physical mechanisms underlying neurite outgrowth: A quantitative analysis of neuronal shape

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 d₅. 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 d₅ of 1. 680. 15. We also propose an explanation of certain stages of neuronal shape development in terms of a diffusion-limited-aggregation model, which predicts d₅=1. 700. 1.