VIII. POWER LAW DISTRIBUTIONS

Self-similarity of the large and small is expressed in power laws in which different sizes and lengths are united. In fractals, for example, there are many more small structures than large ones. Their respective numbers are represented by a power law d istribution, such that the number of objects or events (N) is proportional to size (s) raised to a negative power (a), N = s^-a. A common power law for all sizes demonstrates the internal se lf-consistency of the fractal and its unity across all boundaries.

A power law distribution is a litmus test for self-organization, self-similarity and fractal geometries. The natural world is full of such power law distributions between the large and small: earthquakes, words of the English language, interplanetary d ebris, and coastlines of continents. Each of these power law distributions result from a commonality of laws and processes at all scales.

The separations of the 108 shrines of the Panchakroshi encircling Varanasi appear to have a power law distribution with of a= 1.5. Alternately stated, pilgrims create a fractal time series as they move along the Panchakroshi . The implications of such a power series are potentially profound and revealing. The shrines are neither regularly spaced or randomly scattered, but their sequential placement may obey an organization that is deep, hidden, and yet natural.