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## How to Draw Variations on the Snail Shell Labyrinth, Part 1

The “original” Snail Shell labyrinth was created from the seed pattern for Ariadne’s thread. To do that only the first curve to be drawn had to be shifted one ”unity” to the right. Then all points were connected with each other. Thus a new type for a 7 circuit labyrinth appeared.

However, this type can also be derived from the well-known seed pattern for the walls. The construction goes as usual, only that everything is shifted to the right.
The following drawing shows the walls in black, the seed pattern is highlighted in color.

The Snail Shell Labyrinth made from the seed pattern

In the meantime, Andreas has also posted something to this labyrinth. He has explained the pattern in the labyrinth, and has pointed to the fact that the path crosses twice the axis. Thus, in the terminology of Tony Phillips it is a non-alternating uninteresting Labyrinth.

The ”pattern” is for Andreas not the seed pattern, but the structure of the labyrinth, as best to be seen in the rectangular form.  Hence, “uninteresting” in the terminology of Tony Phillips means that inside this labyrinth the type Knossos is hidden to which only some circuits are added. And the fact that one enters the labyrinth on the first circuit and reaches the middle from the last one.

For me it is interesting that developing the Snail Shell labyrinth from the seed pattern produces the cruising axes. This is ordinarily not the case when using this method. Nevertheless, a new type of labyrinth appears.

If one constructs a labyrinth by only using the path sequence and without cruising the axes, one receives another labyrinth again. Thus it looks:

The Snail Shell Labyrinth made from the path sequence

This is quite an other type of labyrinth, although it has the same path sequence. Moreover, it is self-dual, because you may count the circuits from inside outwards and you will get the same path sequence.
This shows once more that only the path sequence is not sufficient to classify the type. Unfortunately, I must say, because this makes the categorization even more difficult and more complicated.

One receives even more variations if one includes the crossing of axes or chooses other forms (circle, square). Of which more later.

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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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## The Pattern of the Snail Shell Labyrinth

If we dissect a labyrinth along its axis and uncurl it symmetrically on both sides, we can transform it into a rectangular form. The Ariadne’s Thread in the rectangular form is what I refer to as the pattern of a labyrinth. In this pattern, the entrance is at top left and the way into the center at bottom right.

Figure 1 shows this process in abbreviated form for the Snail Shell labyrinth. The labyrinth, represented by its Ariadne’s Thread is dissected along the axis (2 vertical black lines). Both halves of the axis are flipped upwards by half the arc of a circle around the center. By this, the Ariadne’s Thread is transformed from a circular closed form into a rectangular form.

The path of the Snail Shell labyrinth traverses the axis twice. This is indicated with the black circles. When transforming the Ariadnes Thread into the rectangular form, the segments of the pathway that lie on the axis are dissected too and come to lie on both sides of the rectangular form. These segments are drawn as dashed lines in the pattern and also indicated by circles.

Figure 2. Labyrinths Contained in the Snail Shell Labyrinth

In the Snail Shell labyrinth, a Knossos-type labyrinth (single double-spiral like meander) is included. To this are attached at the inside and outside one circuit with the pathway changing direction. Therefore, in the Snail Shell labyrinth, the labyrinth that corresponds with Arnol’d's figure 3 is also included. To this are attached at the in- and outside one circuit without the pathway changing direction. This is where the path traverses the axis. Thus, the Snail Shell labyrinth, in the terminology of Tony Phillips, is a non-alternating uninteresting labyrinth.

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## Labyrinths in Gurudwaras at Nanded (India)

I got the photos and most information in this article from Jagpreet Singh from Mumbai in India. I had like to say a big thank you to him.

He was on a religious trip to Nanded in February 2013.

Jagpreet Singh reported:

I visited nearly 10 – 12 historical Gurudwaras in and around Nanded. Most of the big Gurudwaras in India have geometrical designs in the Parikrama, like the Golden Temple in Amritsar. I was really intrigued when I discovered as many as 7 labyrinths during the Parikramas (the walk around) in the different Gurudwaras.

The commonality in many of these was that they were on the left hand side of the entrance of the Temples. However, all of them were of a different design and size in the center. While some labyrinths were approx. 6 feet by 6 feet, there was one which was approx. 20 feet by 20 feet – a person can actually do the labyrinths’ walk. There was one that was approx. 4 feet by 4 feet also.

As to the material used to make them: All have been made of marble of different colours.

Even though the Gurudwaras are approx. 300 years old, all of them have gone through a major renovation in 2007-2008, (just before the 300 year centenary of the 10th Guru of the Sikhs – Guru Gobind Singh). So I am not sure if the labyrinths are a new addition or have been there all along.

Click into a photo to open the carousel. By clicking the Esc key you can return.

All photos with kind permission of Jagpreet Singh. © by Jagpreet Singh.

On the photos I could identify five different labyrinths. Four follow the pattern shown below, only one deviates from it.

They are square, the entrance is situated on the first circuit which leads clockwise around the whole figure. In the four corners are convexities in angular or circular shapes. From the last circuit one reaches the middle which is a little bigger and is mostly still decorated with geometrical patterns.
The path sequence is: 0-1-4-3-2-5-6-7. One recognises in it the relationship with the classical 3 circuit labyrinth type Knossos.

6 circuit labyrinth with seed pattern

The designers of the labyrinths are (still) unknown, also the intended purpose. Are they pure ornaments or, nevertheless, suited for rituals? Are they influenced by the western culture or from Indian origin?

Maybe somebody knows more about these labyrinths?
In the next Caerdroia Jeff Saward has intended a publication about this and other labyrinths in India. Maybe we get to know then more?