Amazing Labyrinths

Samuel Verbiese
Bridges Donostia: Mathematics, Music, Art, Architecture, Culture (2007)
Pages 405–412

Abstract

Unicursal labyrinths have increasingly gained interest recently, especially among spiritual and esoteric communities all over the world. (Multicursal mazes, also very popular lately, are not discussed here). This paper describes several geometrical and playful aspects, starting from the 800-year-young Chartres labyrinth, which itself is then found stemming from the 5000-year-old “Classical” labyrinth. The unusual Chartres design has been copied in many places and has spawned a number of simpler layouts that echo the original. I present a seven-circuit Chartres look-alike that emerged from a study I conducted four years ago in which most of the features of the original Chartres labytinth have been preserved, thanks to the method I used for its generation. Note that even though I since discovered a variation of this design was built twenty years ago as a maze and that my analysis/generation method was used already, albeit in a different way, I was fortunate I pursued my initial research without knowing this. Some of my work has been devoted to the negative maze content of the Chartres labyrinth, i.e. when the boundary is “walked” instead of the path, it reveals three entry points and three corresponding ultimate goals. A very convincing pseudo-maze can be obtained using an Escher-like visual trick to conceal the topological impossibility of progressively changing some boundaries into paths. I took a further leap to infinity based on a fractal approach, by modeling true 3-D labyrinths on the computer, departing from the so-called 3-D labyrinths that are mere 2-D mappings on shallow surfaces like hilltops. I briefly conducted the latter study for the “Classical” labyrinth, and used KnotPlot advantageously; a few renderings are shown. Finally, I mold this new information into a possible simplified chronologic history of the Chartres design and present more than a dozen novel labyrinths that were mowed in prairies. Three have become permanent.

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