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## The Cretan at the Crossing Point

The Cretan labyrinth is related to other historical labyrinths in two manners. The easiest way to show this is to compare the seed patterns for the Ariadne’s Thread (see related posts below) of these labyrinths. A first line leads from the Knossos- to the Otfrid-labyrinth. For reasons of space, I arrange this in horizontal order and therefore refer to it as the horizontal line. The other (vertical) line leads from the Löwenstein 3- to the Tibble-labyrinth. The first labyrinth in either line is one of the only two existing alternating one-arm labyrinths with 3 circuits.

`  1 / 1                             Löwenstein 3                            1 / 3`
`  Knossos                              Cretan                              Otfrid`
`  3 / 1                              Hesselager                            3 / 3`
`  4 / 1                               Tibble                                4 / 3`

The labyrinths of the horizontal line contain exclusively the single double-spiral like meander (Erwin’s type 4 meander, see related posts below). However, they are made up of a varying number, i.e. 1, 2 or 3 of such meanders. Their seed patterns are composed of a varying number of similar segments. A segment consists of two nested arcs.

• The Knossos-type labyrinth contains one meander. The seed pattern of this labyrinth is made up of two segments. This pair of horizontally aligned segments complete to the meander in the labyrinth.

• The Cretan consists of two meanders that are connected by a circuit between them. The seed pattern is made up of two pairs of segments aligned vertically.

• Finally the Otfrid-type labyrinth is made up of three meanders that are connected by circuits between them. The seed pattern consists of three vertically ordered pairs of segments.

All labyrinths of the vertical line consist of two similar figures that are connected with a circuit between them. They all have a seed pattern made up of four similar quadrants. But the seed patterns differ with respect to the shapes of the quadrants.

• The Löwenstein 3-type labyrinth consists of 2 serpentines. This is reflected in the seed pattern by the four single arcs.

• The Cretan is composed of 2 single double-spiral like meanders (type 4 meander). The quadrants of the seed pattern of this labyrinth consist of two nested arcs.

• The Hesselager type labyrinth is made up of 2 two-fold (type 6) meanders. The quadrants in its seed pattern are made up of three nested arcs.

• Finally, the Tibble-type labyrinth consists of 2 three-fold (type 8) meanders, the quadrants of its seed pattern are made-up of four nested arcs.

The images above are arranged in the form of a table or matrix with 4 rows, 3 columns and 12 fields (frames). Six of these frames contain seed patterns directly related to the Cretan, the others are still void. The relationships of the horizontal and vertical line can also be formulated as follows:

• Progressing (horizontally) one column to the right will increase the number of meanders by one.
• Progressing (vertically) one row downwards will increase the depth of the meander by two. The depth of a meander corresponds exactly with it’s type number – a type 4 meander has depth 4, a type 6 meander depth 6 a.s.f.

With this information we are able to add the missing seed patterns and the corresponding labyrinths. By doing so we will encounter two other historical labyrinths and one figure that is no labyrinth. Of course it is also possible to add more rows or columns to the table and to fill the new frames with the corresponding seed patterns. All figures generated this way are self-dual. The figures of the first row are, in the terminology of Tony Phillips, uninteresting, all other figures are very interesting labyrinths (see related posts below).

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### 2 Responses

1. […] labyrinth straight away. And this applies best to the seed patterns of the Cretan type labyrinth and its relatives of the vertical […]

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2. […] single double-spiral-like (Erwin’s type 4) meanders. These are the three labyrinths of the horizontal line of the labyrinths directly related with the Cretan […]

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