the truth is fractal and far from simple

To better understand growth mechanism (and defusion), examining thin film deposition interfaces growth leads us to features that have tendency towards spherical symmetry as in fractal curves, similar to many growing interfaces in nature and biology such as fluid flow in porous media, adatom and vacancy islands on surfaces, atoms at borders of crystalline facets, bacterial growth, wetting fronts, etc. Their geometry evolves exponentially – that is a matter of great concern in scaling which is dynamic in nature. Surface diffusion show transition from smooth to unstable growth. Some studies prove initial stability of ordered structures in growth may result in instability at longer times which ends to epitaxial breakdown. Such dynamism in growth has great implications in medicine, such as tumour growth and in semiconductors as it concerns crystal growth. It may have implications on self assembly methods.

http://www.ox.ac.uk/media/science_blog/080328.html

Ref.:
Carlos Escudero, Dynamic Scaling of Non-Euclidean Interfaces, Physical Review Letters, Vol 100, 116101 (21 March 2008)
http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRLTAO000100000011116101000001&idtype=cvips&prog=normal
Haselwandlter C A, Renormalization of stochastic lattice models: Epitaxial surfaces; ISI Web of Knowledge; Physical Review E, Vol 77 Issue 6, June 2008
Escudero C, Geometric principles of surface growth, PHYSICAL REVIEW LETTERS Volume: 101 Issue: 19