Potential mytho-poetic implications

Psycho-social Significance of the Mandelbrot Set (Part #3)

Insights distinguishing levels of abstraction, of the same subtle order as the M-set, may have been deliberately (or inadvertently) anchored in cultural artefacts such as myths, legends, leys and the like. Whether they are termed "archetypes" or not, their fundamental nature and importance is nourished by the societies by which they are valued for the order they offer.

Examples of the possible relationship between such cultural artefacts and the form of the M-set include:

Two dragons chasing a pearl: The decorative art of China, including temples and traditional folk dances, focuses extensively on the theme of two dragons. They are usually depicted facing one another in the air in eager pursuit of a spinning pearl floating like an iridescent bubble between them. This theme was a mark of books issued under imperial auspices. For Taoists, the complex associations of that pearl include wisdom, yang energy, truth and life -- even the everlasting life of those who perceive the truth and attain enlightenment. The pearl can also be thought of as a symbol for universal Qi energy -- the progenitor of all energy and creation. The two dragons are associated with an understanding of eternity. The Chinese have a belief that they themselves are "descendants of the dragon". Given their "protuberances and jewelled scales", the two dragons can readily be associated with the two sides of the M-set representation -- in pursuit of the circular 2-period ball.
Two dragons of Arthurian mythology: These supposedly represent the two aspects of the British nation: the red one Celtic and the white Saxon.
Ba Gua (Pa Kua) and associated dragons: The 8 basic trigrams of the I Ching, in their traditionalcircular disposition (discussed below), have also been associated with the nine classic dragons of China [more]. Each of these symbols can be understood as guarded by dragons, each with distinct personalities and powers. As a set they protect the insights represented by the cardioid region of the M-set.
"Here be dragons": It is perhaps trivial to recall that ancient maps had a tendency to mark the outskirts of maps of the known world with phrases like "here be dragons". It is indeed the case that what can be known, or "remembered", in any permanent sense might be said to be represented by the boundary of the M-set.
"Sword in the stone": This basic Arthurian myth regarding the sign of true royalty might well be associated with the understanding of how to distinguish, or grasp, the sword-like axes effectively embedded within the chaotic stone-like structure of the M-set representation.
"Withdrawing into the stones": This Irish Celtic myth recalls the story of an elder race (the Tuatha Dé Danaan) that through their wisdom were eventually able to "withdraw into the stones". There is now extensive modern myth-making in relation to "intraterrestrials" at another "vibratory level". Do some implications of mediational insight suggest that people can withdraw into the "fabric of reality" as embodied in the dynamics encoded by the M-set?

In each case, these myths might also be understood as an ability to function at the level of abstraction mapped by the domain of the M-set, again to be understood as a form of stone.