The relationship of the Middle Way, the Tao, and Jung s Transcendent Function to the recurring mandala shape of the circle has been historically a matter of intuition by practitioners of these principles. Surprisingly, it is also a mathematical fact - easily demonstrable by examples using a computer spreadsheet with charting functions. If one makes a graph of randomly placed points and joins them by lines, one finds a diagram like the one below. The graph very much resembles a jumbled combination of psychological polarities, confusion, and unrelated-ness. This process repeats until all the original lines are replaced.
Some cases eventually form a more circular pattern.
The shape of the charts also suggest a plant or flower unfolding in an organic manner and is a way of visualizing the unfolding of the personality. I cannot provide proof that for all starting conditions an enclosed shape must be created. All rights reserved. Davis,P.J., Circulant Matrices.