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Center for Nonlinear Studies |
Some fascinating natural shapes present cauliflower-like structures. Surfaces of thin films, turbulent and combustion fronts, geological formations or biological systems are strikingly similar in spite of their diversity. In all cases, one can recognize a typical motif independently of the scale of observation. These appealing morphologies combine two apparently contradictory features: a hierarchical (fractal) structure and disorder (randomness). Fractal geometry is a useful tool to describe natural shapes but, to gain physical insight a theoretical framework that describe the way that they can be produced is needed. We present a compact dynamical equation for evolving surfaces that produces cauliflower-like structures and has a large degree of universality. This nonlinear equation allows us to identify non-locality, nonconservation and randomness, as the main mechanisms controlling the formation of these ubiquitous shapes. To test our theory at different scales, we have grown thin film nano-structures by Chemical Vapor Deposition and measured the scaling properties of (centimeter size) cauliflower plants. These experiments allow us to establish, quantitatively, the domain of validity of the equation.
Host: Luis M. A. Bettencourt