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Posts Tagged ‘snail shell labyrinth’

Some time ago I already posted a walkable Babylonian visceral labyrinth (see related posts below).

Today I will present another one.

Babylonian Snail Shell Labyrinth

Babylonian Snail Shell Labyrinth

I have called it snail shell labyrinth because it reminds me of one. In addition to that I have also extended the entry area on the left a little bit wave-shaped.

It is a new type of labyrinth again: It has an unequivocal way through a labyrinth, not into a labyrinth. Therefore there are two entrances, no center to stay in or to return from.

I have written about the labyrinth and the origin quite detailed (see related posts below). The illustration on the clay tablet VAT 9560_5 of the Vorderasiatisches Museum Berlin forms the basis of the layout. Hewre we deal with a walkable implementation.

The following drawing shows the main elements.
At first one should fit the labyrinth into the available locality and determine the orientation. To achieve that one defines the points M3 and M5.

The main elements

The main elements

By use of triangular measurements from two points the other salient points are determined. One do not necessarily need to define the beginning and the end of each curve in advance. They lie on the (imaginary) lines between the main points or along the extension about these points.

If one puts on the semicircles in the right part first (in Blue) using M4 as midpoint, one has already created a large part of the arcs and can then add the other pieces.

As to the five curves around M3 one must pay attention that only the most internal two semicircles are continuous, the three external ones only reach up to the line determined by the points M3-M1-M6.

One could also form the entry area around M6 in a different way.


The exact measurements of the entire labyrinth are found in the layout drawing below.

The following layout drawing is a sort of prototype with the dimension of 1 m between  the axes which also corresponds to the distance from line to line. The remaining measurements arise from this definition and the shape of the labyrinth.

The construction is scaleable. This means, all other desired path widths can be derived from it.

If e.g., a path width of 60 cm is desired, one takes the factor 0.6. All other measurements of the drawing are calculated with this factor, i.e. the road length as well as the line length, the main dimensions, the radii, the oblique distances of the centres etc.

Layout drawing

Layout drawing

Two examples:

One labyrinth sprayed on the lawn in the garden of Gundula Thormaehlen Friedman in Bad Kreuznach.

One painted with chalk on the plaster of the parking area in front of our flat in Würzburg. The children of the surroundings had a lot of fun and were running it tirelessly.

By the way, one can also walk the labyrinth hand in hand. After the first round the partner starts in the upper entrance. In the meander of the middle one meets and changes the paths.

Here the layout drawing as a PDF file to watch/print/copy/save (for non- commercial uses only) …

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The Snail Shell Labyrinth

The labyrinth next to the Cretan is the Snail Shell labyrinth. These two labyrinths have the same seed pattern. And they are the only ones with this seed pattern. Well, how then do we draw a Snail Shell labyrinth in the Man-in-the-Maze (MiM)-style? Very simple: we just use the Cretan labyrinth in the MiM-style from our last post (see related posts below). This labyrinth rotates clockwise.

The Cretan labyrinth in clockwise rotation

The Cretan labyrinth in clockwise rotation

And now let’s rotate the seed pattern, whilst keeping everything else in place.

The Snail Shell labyrinth in clockwise rotation

The Snail Shell labyrinth in clockwise rotation

Rotating it by one step in anticlockwise direction connects the center to the next intermediate space on the same quadrant of the seed pattern. This generates the Snail Shell labyrinth in clockwise rotation.

The Snail Shell labyrinth in anticlockwise rotation

The Snail Shell labyrinth in anticlockwise rotation

If we rotate the seed pattern one step further, the center is connected to the second next intermediate space. This again generates a Snail Shell labyrinth, however in anticlockwise rotation.

The Cretan labyrinth in anticlockwise rotation

The Cretan labyrinth in anticlockwise rotation

And if we rotate the seed pattern one more step further, we will receive the Cretan labyrinth again, but also in anticlockwise rotation.

The MiM-style thus provides an actual layout of a labyrinth which enables us to do exactly the same as we did here on a more theoretical base, i.e., to rotate the seed pattern (a more detailed description of the whole process is provided here). This theoretical analysis was performed using the seed pattern for the Ariadne’s Thread of the Cretan-type labyrinth. It predicted, that by rotating the seed pattern, only two different figures – the Cretan and the Snail Shell labyrinth – could be generated, each of them in clockwise and anticlockwise rotation. With the MiM-style labyrinths we have now an empirical proof of this result. Of course, it does not matter, whether the seed pattern for the walls or for the Ariadne’s Thread is used. Both lead to the same result although represented either by the walls or by the Ariadne’s Thread. In my theoretical analyses I prefer to use the representation with the Ariadne’s Thread as it is easier to read than the representation with the walls.

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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. From the Ariadne's Thread to the Pattern

Figure 1. From the Ariadne’s Thread to the Pattern

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

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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Readers who have been visiting this blog for some time, will know the following figure.

Figure 1: Snail Shell Labyrinth

Figure 1: Snail Shell Labyrinth

Erwin calls it the Snail Shell Labyrinth. He had generated this labyrinth by completing the seed pattern for the Ariadne’s Thread of the Cretan-type labyrinth. But instead of the usual end he completed it around an other one of its ends. So he did, what I refer to as shifting the center. Somebody else also had the same idea, as can be seen in this source on page 14 (scroll down on the link page). Both shifted the center to a neighbouring end in the same quadrant, but did not continue with this process.

What might be unknown to the most is, that the Snail Shell Labyrinth is the only other figure that can be generated by rotating the seed pattern of the Cretan. With the statements from my previous posts about the shifting of the center (see related posts below), we are able to demonstrate this.

Figure 2: Seed Pattern

Figure 2: Seed Pattern

The seed pattern for the Ariadne’s Thread of the Cretan has 16 ends (fig. 2). So there are 16 possibilities to place the center. However, these reduce to four, as the seed pattern is made up of four similar quadrants. After four rotational steps, the seed pattern is self-covering.

Figure 3: Symmetry

Figure 3: Symmetry

In addition, each of these quadrants is symmetric in itself (fig. 3). This reduces the range of figures to two pairs. Each pair is made up of the same figure rotating either clockwise or anti-clockwise.

Figure 4: The ends and the pairs of figures

Figure 4: The ends and the pairs of figures

This is shown in fig. 4. Connecting the first end with the center generates the first figure in clockwise rotation. I therefore label this end as 1 →. If we connect the second end with the center, this generates figure 2, in clockwise rotation (2 →). The third end connected to the center generates also figure 2, although in anticlockwise rotation (← 2). And finally, the fourth end generates figure 1 rotating anticlockwise (← 1). Figure 1 is the Cretan, figure 2 the Snail Shell Labyrinth. We now have completed the first quadrant. The fifth end of the seed pattern is the first of its second quadrant and with this, the whole process begins anew.

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