VII. FRACTALS
Fractals are composed of self-similar structures and have overall geometries with fractional dimensions. The well-known fractal named after Mandelbrot is a striking example of the endless inclusion of patterns within patterns. No matter how much its ti niest element is magnified it still contains the essence of the entire structure. Fractals are the free spirits of the world of mathematics and geometry and range in the natural world from clouds, cauliflowers, leaves, braided streambeds, and coastlines ( Porter and Gleick 1990; McGuire 1991). It should come as no surprise that pilgrimage landscapes have fractal geometries when their geometric patterns are generated by the natural movement of people.
Meyer (1994) suggests that "psychic maps" and cosmograms are created by most cultures and are "absorbed and held unconsciously by members" of those cultures. Mentally-held cosmograms may often be elements of the pilgrimage experience as pilgrim s move along fractal pathways of their own. The complex geometry of the Hindu yantra is an example of such a mental map, which holds great power and significance for the Hindu pilgrim and which may play a role in organizing the ideal landscape thro ugh which pilgrims move (Khanna 1979).