Relevance of Percolation Theory to Power-Law Behavior of Dynamic Processes Including Transport in Disordered Media P ower-law behavior seems ubiquitous in nature as well as in human endeav- ors. Flood statistics [1–5], water storage [6], drainage basin organization [7], relationships between channel dimensions and flow [8], extreme precipita- tion events [9], wind and weather fluctuations [10, 11], stock and commodity mar- kets fluctuations [12, 13], income distributions [14, 15], music [16], language [17– 20], (non)coding DNA [21], earthquake statistics [22–24], landslide occurrence [24, 25], electrical conduction in disordered media [26], particle-size distributions in soils and rocks [27–29], cities [30], species distributions [31], internet topology [32], etc., have all been noted to obey various power laws. Many physicists have searched for unifying concepts to explain such ubiquity. Perhaps, however, power- law behavior is not quite as universal as thought. Multifractal distributions origi- nating from cascade processes as a related, but somewhat more complex, organiz- ing principle have often been proposed to be the appropriate universal description [33, 34]. Some [35–37] have questioned whether a ‘‘class’’ of stretched exponential functions might better represent a larger or smaller fraction of the data. In the ac conductivity of disordered insulators, for example, several other frequency- dependences [38–40], universal or not, have been suggested. This small sample of alternate ideas need not imply that alternative scenarios are always correct either. But simply because it is often asserted that nature follows power laws does not require such; in most cases the range and quality of data are probably not suffi- cient to distinguish the subtle differences between the various proposed distribu- tions. But the recognition of the simplicity of the explanation that self-similar geo- metrical structures [41] could be the basis of so many geophysical manifestations of apparent power laws has certainly provided impetus to the interpretation that a large number of natural phenomena do follow power-law behavior. In the case that one believes that the observed behavior conforms to true power laws, what kind of underlying mechanism should one seek? At least six such unifying concepts, nonlinear dynamics (chaos) [42], self-organized criticality [43], hierarchical dynamics [44], highly optimized tolerance [45], minimum effort ALLEN HUNT Allen Hunt is with the Departments of Physics and Earth and Environmental Sciences, Wright State University, Dayton, Ohio 45435 (e-mail: allen.hunt@wright.edu) Q 2009 Wiley Periodicals, Inc., Vol. 15, No. 2 COMPLEXITY 13 DOI 10.1002/cplx.20267 Published online 5 August 2009 in Wiley InterScience (www.interscience.wiley.com)