The classic Cretan/Thesean labyrinth is an ancient
pattern found all over the Mediterranean world. Possibly derived
from ritual or dance movements, the pattern involves a set of
identical turning patterns, each of which is a triad of left-right-left
movements. The fractal quality of this combination of twists and
turns suggests that W. F. Jackson Knight was essentially correct
when, in Cumaean Gates, he connected the labyrinth with
the 'problem' of separating the realms of the living and the dead.
The labyrinth is equivalent to verbal formulae used in encomia
and curses - words arranged to provide passage and at the same
The labyrinth is almost a literal image of the bolagram. Its twists - a combination of physical and psychical 'violations' of the customary set of spatial relations - are what might be regarded as a two-dimensional version of the a-dimensional topography of the Möbius band. Implicit at every level and step of the labyrinth is the unresolvable dialectic between the immanence of movement and the transcendence of the idea of a possible plan. W. H. Auden, in the poem, 'The Labyrinth,' wrote:
Anthropos apteros, perplexed
To know which turning to take next,
Looked up and wished he were the bird
To whom such doubts must seem absurd.
The relationship between labyrinths and fractals has been suggested but not explored decisively. Fractals are self-replicating forms characteristic of 'recursion' and 'self-reference.'
This analysis parses the labyrinth into its 3+3 constituent curves. Combining them produces the same pattern on the 'next highest' level. The anecdotal connection of the labyrinth to questions of self-knowledge and monadic conditions is confirmed by the use of a fractal design.
In turn, it might be productive to re-assert the bolagram's essential fractal nature - its ability to relate to issues of both parts and wholes and the relationships between parts and wholes.
© 2012, Donald Kunze, all rights reserved