Fractal Electrodynamics and Modeling

Since nature has provided us with structures of almost infinite complexity and variety, it is apparent that some, and perhaps most, of these structures cannot be treated by traditional deterministic methods when modeling their interaction with electromagnetic waves. As one alternative, average properties of these interactions can be treated through statistical means and the use of averages and higher-order moments. These conventional methods are particularly successful when the scales of these structures are limited to modest ranges of variation or to the case of resonant interaction. However, certain types of wildly irregular, ramified, or variegated structures contain many scale sizes as demonstrated in the fractal surfaces of Fig. 1. It is often difficult to characterize the interaction of waves with these structures and in many cases it is not even easy to model these structures. It is just these complicated structures which are of interest to us here and which can often be modeled by the use of fractals. Thus, we blend fractal geometry and electromagnetics in a discipline we call fractal electrodynamics [1].