Understanding Complexity: A Geometric Perspective

Carlos Puente (cepuente@ucdavis.edu), Department of Land, Water, and air Resources, UC Davis, and Andrea Cortis Lawrence Berkeley National Laboratory

We present a deterministic geometric procedure that provides a wide range of complex-looking patterns over one, two and three dimensions. These patterns are generated by means of a procedure that transforms multifractal measures via fractal functions. It is shown how this simple procedure may be used to generate distributions that closely resemble observed natural patterns such as rainfall sets and contaminant plumes. We illustrate how these deterministic patterns evolve as a function of their generating parameters, and how these evolutions may provide a novel insight in the characterization of natural phenomena. Finally, the mathematical and physical implications of this geometric procedure are discussed together with startling results related to the Gaussian distribution limit.