How to Draw the Eight 5 Circuit Labyrinths

There are, as now everybody knows, 8 different possibilities for a 5 circuit, one-arm labyrinth (where the axis is not crossed).

Tony Phillips has furnished evidence for this on his website. He is a Professor of Mathematics at the State University of New York and he approaches mathematically to the question.

Some of these versions are known and were already built as labyrinths to walk. But some just not. Andreas Frei has already shown these 8 types. Tony Phillips describes the curves of the Russian mathematician Arnol’d which lead exactly to these variations.

Now I would like to introduce once again all 8 variations. In the meantime, I have developed a method to construct a labyrinth according to the path sequence. This path sequence is also a good name and a differentiation sign for a certain labyrinth type.

The different labyrinths are not developed from the well-known pattern. Even not from the pattern for Ariadne’s thread.

The figures of the eight labyrinths, first in round shape and with a bigger middle, then in square form. The contained pattern is emphasised in colour. Indeed, it has been determined after the construction of the labyrinth. The ways and the boundary lines are equally wide. The path sequence should serve as a marking of the type.

0-5-2-3-4-1-6

0-5-2-3-4-1-6

0-5-2-3-4-1-6

0-5-2-3-4-1-6

0-3-4-5-2-1-6

0-3-4-5-2-1-6

0-3-4-5-2-1-6

0-3-4-5-2-1-6

0-1-2-5-4-3-6

0-1-2-5-4-3-6

0-1-2-5-4-3-6

0-1-2-5-4-3-6

0-3-2-1-4-5-6

0-3-2-1-4-5-6

0-3-2-1-4-5-6

0-3-2-1-4-5-6

0-5-4-3-2-1-6

0-5-4-3-2-1-6

0-5-4-3-2-1-6

0-5-4-3-2-1-6

0-5-4-1-2-3-6

0-5-4-1-2-3-6

0-5-4-1-2-3-6

0-5-4-1-2-3-6

0-1-2-3-4-5-6

0-1-2-3-4-5-6

0-1-2-3-4-5-6

0-1-2-3-4-5-6

0-1-4-3-2-5-6

0-1-4-3-2-5-6

0-1-4-3-2-5-6

0-1-4-3-2-5-6

Here some more explanations to the path sequence: The paths inside a labyrinth are numbered from the outside inwards, to the center. The order in which the paths are walked from the entrance up to the middle displays the path sequence. The digit “0” stands for outside (or beginning) and the last number marks the center itself.
The first number after “0” must always be an odd number, so 1, 3, or 5 (and so on). Otherwise it does not work.
The row of numbers must be composed of alternating even and odd digits. Otherwise it will not be a labyrinth. The mathematician expresses this differently, but for us this information should be enough.

Who would like to build a new 5- circuit labyrinth, can get here suggestions.
I personally like the second variation with the path sequence 0-3-4-5-2-1-6 best of all. Who builds it?

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2 thoughts on “How to Draw the Eight 5 Circuit Labyrinths

  1. Pingback: The 5 Circuit Labyrinth on Rubik’s Cube | blogmymaze

  2. Pingback: A new Generation of Sector Labyrinths | blogmymaze

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