Self-organizing systems are characterized by self-similarity and scale invariance. Similar geometric patterns are repeated at different sizes and are expressive of a fundamental unity of the system. The "physics" is continuous across multiple layers of scale; the same processes of nature reoccur at different levels. With no fundamental scale or characteristic size, self-similar structures are unchanged after increasing or shrinking their size. The parallelism of macrocosm and microcosm is a deep and an cient human insight which led the first naming of night-time constellations as well as to astrological speculation. The self-similarity of macrocosm and microcosm is alluded to by Wheatley (1971) when he speaks of "an intimate parallelism between t he regular and mathematically expressible regimes of the heavens and the biologically determined rhythms of life on earth….."

Pilgrimage systems are replete with self-similar structures. The pathway walked by the pilgrim may represent the universe from center to periphery and may mimic the entire age of the universe from beginning to end. The cosmic cycles which entrain the pilgrim are similar to the cycles of birth, maturation, and death of terrestrial life. Since they can be enlarged or decreased without changing their essence, the geometries of pilgrimage, whether held in the mind of a pilgrim, dr awn on the page of a manuscript, or embedded in a pilgrimage landscape retain their universal meaning.

The cardinal dhamas, the four "abodes" of the gods of the subcontinent parallel the cardinality of the Hindu temple. Varanasi-Kashi is a paradigmatic example of self-similarity. It contains those four dhamas within itself as well as most if not all of the other pilgrimage destinations that span the sub-continent (Eck 1983; Singh 1993; Saraswati 1985). Kashi is one of the Seven Cities, saptapuri, and it achieves another form of self-similarity by including the other six cities withi n itself. The Panchakroshi route encloses the universe, but it is also contained within the body of the individual pilgrim.

The cosmic mountain that the pilgrim circumambulates may be both the axis of the universe and the spire of a temple; a change in scale does not change the significance or efficacy of the movement. The garbhagriha of the temple is both the dark a nd watery womb of life and the point of creation from which the universe expanded outward from chaos. Circulation about the temple may be revolution about the cosmic axis, the motion of the sun in the sky, and a spiral backward in to the beginning of time . The labyrinthine patterns in the floors of certain Gothic cathedrals through which penitents would crawl were meant as miniaturized pilgrimage journeys to the center. The 660 ft circumambulation path at Chartres cathedral symbolically recreates the pilg rimage to Jerusalem (Barrie 1996).

Self-similarity is the key to the story of Shiva and Parvati asking their two sons to demonstrate their love by racing each other around the universe. Ganesh circumambulates his parents, who are also the entire universe, while his brother begins the im mensely long journey along its perimeter. Both pathways are equally valuable and meaningful for the pilgrim, each providing different benefits.