Labyrinth Tiling

A note on ancient labyrinths

Anthony Phillips writes in "The Topology of Roman Mosaic Mazes", Leonardo, vol. 25, no. 3/4, pp. 321-329, 1992:
Floor mosaics were a common form of interior decoration in Roman times, and a maze pattern was a perennial theme... these mazes are unicursal (without bifurcation)...

We have no record of the work that went into developing this concept, but there is a related class of figures going much farther back in history: various forms of the famous Cretan maze. The earliest illustrations of this maze that can be securely dated are a pair of figures on a clay pot from Tell Rifa'at, Syria (dated before 1200BC) and a doodle scratched on the back of a clay accounting tablet in King Nestor's palace in Pylos (Western Greece) and hardened by fire when the palace burned down around 1200BC). ... The game of drawing this nucleus and completing it to a maze is still played today. ...

Once the mazes are unrolled, it bicomes obvious that they are intimately related to, and perhaps derived from, the meander patterns ubiquitous in primitive decoration. It should be noted that meanders and mazes appear interchangeably on the earliest coins from Knossos ... suggesting strongly that [these forms] were equivalent symbols for the Labyrinth.

... every Roman mosaic maze that has survived intact is a meander maze, and I will make the case that the mazes that do not appear to be of this type fail to do so because of faulty restoration or recording.

Labyrinth tiling, David Eppstein, ICS, UC Irvine.
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