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Recently Erwin informed me, that a new comment had come in to one of his older posts: „Is there an easy way to draw the ‘man in the maze’ labyrinth?“ I was about to answer in the comment box, but it turned out that it was not that easy. However, there is a sure way, and this is not really difficult either. Two elements are needed for this purpose: An auxiliary figure and the seed pattern. Let us have a closer look at what this means, using the labyrinth presented by Erwin.

The Native American Labyrinth

The Native American Labyrinth

As Erwin correctly notes, this is a labyrinth of the Cretan type. All the walls are arranged in a strict geometric order. They all lie on a special grid. This is made-up of a wheel with 11 concentric circles / rings and 16 spokes.

The Auxiliary Figure

The Auxiliary Figure

This grid is the auxiliary figure we need. In his drawing, Erwin has numbered the circuits of the labyrinth from 1 through 10 with the (not accessible) middle being number 11. This same enumeration can also be applied to the walls. These lie on the rings of the grid. Then, the outermost ring has the number 1, the innermost ring number 11.

The second element we need, is the seed pattern. As we want to draw the labyrinth represented by the walls, we also need the seed pattern for the walls of the labyrinth. And, since it is a labyrinth of the Cretan type, we need the seed pattern of the Cretan-type labyrinth.

The Seed Pattern

The Seed Pattern

The seed pattern is first varied such that it fits to the auxiliary figure. All the lines and dots must lie on the grid. Compared with some earlier variations, this is only a slight variation. It is immediately recognizable as a seed pattern of the Cretan type. This is now placed in the middle of the auxiliary figure. The 16 ends of the seed pattern are formed by the intersection points of the 16 spokes with the 9th ring.

The First Step

The First Step

Now it remains to complete the seed pattern to the whole labyrinth. For this, first, the situation of the center of the labyrinth has to be determined. Then, we proceed exactly as described here. First, the two ends next to the center are connected. However, this is not done with an arc around the center, but using segments of lines that lie on the grid provided by the auxiliary figure. By this we draw the innermost wall of the labyrinth.

The Second Step

The Second Step

We then continue with the ends next to first connection and create the second inner wall.

The Third Step

The Third Step

Then follows the third connection in a similar way, and likewise all others follow. And by this, from the inside out, one wall is added after each other.

The Complete Labyrinth

The Complete Labyrinth

Finally, one opening remains. This is the entrance to the labyrinth. If we then remove the auxiliary figure, we can easily view the final result.

Labyrinth without Auxiliary Figure

Labyrinth without Auxiliary Figure

This guidance shows the importance of distinguishing between the type of a labyrinth and the layout. We have here drawn a Cretan-type labyrinth on a Man-in-the-Maze layout, or, let’s say: in the Man-in-the-Maze style (MiM-style). Every type of a one-arm labyrinth can be drawn in the MiM-style.

The type of a labyrinth can be entirely represented by the seed pattern. This, actually, is the meaning and purpose of the seed pattern, that it contains the essence of the whole labyrinth.

In my previous posts I have followed variations to the Cretan type labyrinth and examined their effects on the shape of the seed pattern. Some variants were found, that varied the seed pattern in such a way, that it was hardly recognizable and practically useless.

Here I come back again to the original purpose of the seed pattern. In this case, where we want to draw a labyrinth in the MiM-style, the seed pattern is of essential practical use. Without it, I see no easy way. But using the seed pattern on the auxiliary figure, with some skills, it is even possible to draw a labyrinth freehand in the MiM-style.

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The Nîmes labyrinth is of the Cretan type although with a very special layout. The layout of the Cretan can be transformed in five steps to the Nîmes labyrinth. This is shown in the following illustrations. The figures on the left side show the starting point, whereas the right figures show the next step. In the right figures, the base situation is coloured in grey, the action in red and the result in black.

Illustration 1. First Step

Illustration 1. First Step

Ill. 1 shows the Cretan on a quadratic centered layout as the starting point (0). The center is somewhat enhanced; its height and width are 4 circuits wide. The reason for this is, that it enables us to bend all circuits 4 times by a quarter of a circle. By this, all opposite turns of the pathway are aligned along the axis and oriented vertically. (It is also possible to start with a rectangular layout with the center being 2 circuits high and 4 circuits wide. However, if we narrow the center to a size of 2 circuits in horizontal and vertical direction, the inner circuits of the labyrinth cannot be directed fully around the center and their turnpoints will be oriented horizontally.) As a first step (S 1), the opposite side of the axis is bent downwards 1/4 of an arc around the center in anticlockwise direction.

Illustration 2. Second Step

Illustration 2. Second Step

Ill. 2 shows the result of this step (R 1): A 3/4 labyrinth layout which does not cover the fourth quadrant. (Furthermore, the center is not closed, but this can be neglected here.) This result forms the starting point to the second step. In this step (S 2) we have to create space to be able to shift the inner circuits into the second quadrant. For this, the circuits have to be prolonged to the right by two units.

Illustration 3. Third Step

Illustration 3. Third Step

The result of the second step (R 2) can be seen in ill. 3. The labyrinth has now a rectangular (landscape) layout with wider interior space. In a third step (S 3), the lower circuits are shortened and the third quadrant is partly shifted into the interior space, so that the vertical wall between its 4th and 5th circuit aligns vertically with the upper axial wall.

Illustration 4. Fourth Step

Illustration 4. Fourth Step

Ill. 4 shows the result of this operation (R 3). Here, the final layout becomes recognizable. The center is still open, but one can guess how it will be closed. And this is what happens in the next step (S 4). For this, the lower half is shifted upwards by two units so that the lower horizontal bar comes to cover with the upper horizontal bar.

Illustration 5. Fifth Step

Illustration 5. Fifth Step

Ill. 5 now shows the labyrinth of Nîmes almost completed (R 4). It can be seen, that the exception, where the pathway makes the only additional bend of 1/4 of a circle before it reaches the center (see point 6 of my last post, related posts below), is a result of the transformation process. Now the only thing remaining is to prolong the four outer circuits upwards into quadrant 4, what is performed in the fifth step (S 5).

Illustration 6. The Final Layout

Illustration 6. The Final Layout

So, here we are. Ill. 6 shows the final labyrinth of Nîmes. All transformations only affect the layout of the labyrinth. None of the steps changes the level sequence of the pathway. Therefore the type of labyrinth remains the same throughout the whole transformation process.

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In my last post I have pointed to the special layout of this roman mosaic labyrinth (see related posts below).

Figure 1. Mosaic labyrinth of Nîmes

Figure 1. Mosaic labyrinth of Nîmes

In the meantime I had a closer look at it and found six peculiarities.

Figure 2. The Peculiarities

Figure 2. The Peculiarities

  1. Here, there is no diagonal (as opposed to the 3 fine dashed lines from the middle to the other three corners). Along each of these diagonals, the pathway is bent by 90° degrees. Therefore, all circuits only make three bends of 1/4 of a circle.
  2. Accordingly, the turns of the pathway that normally lie beyond the axis (on the side opposite to the entrance) are oriented horizontally, not vertically.
  3. Moreover, they are not arranged in one line as normally, and as are the turns of the pathway on this side of the axis too.
  4. The three inner circuits (circuits 5 – 7) lie entirely on this side of the axis and thus cover only quadrants 1 and 2.
  5. Correspondingly, quadrants 3 and 4 are only covered by the four outer circuits (circuits 1 – 4).
  6. And, as if this were not enough, the center makes one exception. Instead of entering the center axially, the pathway makes one additional turn of 1/4 of a circle before it reaches the center. Therefore it enters the center in parallel with the way into the labyrinth. First I thought, the designer might have wanted to mislead the observer about the true 3/4 – nature of this labyrinth. A closer look at it, however, reveals, that this last turn of the pathway is an inevitable result of the chosen layout for the course of the pathway.

It surprises me again and again how interesting some of the historical labyrinths are.

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Variants of the Cretan Labyrinth

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The Cretan is the most frequently encountered type of labyrinth, and so for this type we can find a broad range of individual variants. Here I want to show some examples that are of particular interest for various reasons. Unless stated otherwise, all figures are sourced from the book Through the Labyrinth by Hermann Kern. The details can be found here.

Figure 1. Pylos

Figure 1. Pylos

This graffito on a clay tablet from Pylos dates from 1200 BCE at the latest and is the oldest securely dated labyrinth. It shows the Cretan-type on a rectangular layout.

Figure 2. Silver  coin, Knossos

Figure 2. Silver coin, Knossos

This figure shows the labyrinth with a concentric layout on a silver coin from Knossos, ca. 190 100 BCE. The center of the labyrinth covers with the middle of its circuits. The axis, however, is somewhat eccentric, as the pathway reaching the center is aligned centrally.

Figure 3. Walahfrid

Figure 3. Walahfrid

On this drawing from a parchment manuscript by Walahfrid Strabo (808-849), the labyrinth is shown in full concentric form. The axial wall that connects the innermost with the outermost wall of the labyrinth is aligned centrally with the center.

The following examples show, that variants of the layout are not limited to standard forms, such as circles or rectangles.

Figure 4. Heart labyrinth

Figure 4. Heart labyrinth

This heart-labyrith by Mario Höhn is of the Cretan-type, although with an additional closed circuit at the inside. Not all circuits are in parallel course (as with a supposed 7-lane roundabout). Circuits 7 and 6 are limited to the right heart chamber. Circuit 5 leads to the left chamber, where it is connected with the closed 8th circuit.

Figure 5. Double labyrinth

Figure 5. Double labyrinth

An other method to generate a heart labyrinth was used by Marty Kermeen and Jeff Saward. They apply a double labyrinth (DL). This is made up of two identic labyrinths (L) that are mirrored horizonally and connected to each other. So the actual labyrinth is one of these two part-labyrinths. This is a Cretan-type projected on a half-hearted layout.

Figure 6. Abhuyumani Tantra

Figure 6. Abhuyumani Tantra

This tantric drawing from Rajasthan, India, 19th century, shows the labyrinth arranged on three quarters of a circle – most of it actually is unrolled to a semi circle. Only the turn from the first to the fourth circuit covers the whole third quadrant. The fourth quadrant is not covered by the figure.

Figure 7. Nîmes

Figure 7. Nîmes

This roman mosaic labyrinth from Nîmes, France, 1st century, has an inconspicious rectangular outline. But, like no other, it shows that the layout of a labyrinth is not only limited to its outline (circle, rectangle, heart, etc.). It is also important to consider how the course of the pathway is organized within this outline form. And this is really tricky. Just try to identify the seed pattern of this labyrinth. The course of the pathway is special in at least three points.

  • All circuits do not rotate by a full (360°) but only a 3/4 (270°) circle. This is the same as with the Indian labyrinth described above. It is a sort of a 3/4 labyrinth. However, the layout covers all four quadrants.
  • The inner circuits are completely embedded in quadrants 1 and 2. Normally all circuits cover all quadrants.
  • Only the outer 4 circuits cover all quadrants.

These shiftings and transformations vary the layout of the labyrinth so that it is barely recognizable.

But what makes me classify all these different examples as Cretan-type labyrinths? What do all these have in common? What defines a Cretan-type labyrinth has been repeatedly described on this blog and elsewhere:

  • One-arm labyrinth
  • alternating, i.e., the pathway does not traverse the axis
  • 7 circuits
  • level sequence: 3-2-1-4-7-6-5.

It is important to keep in mind that we are dealing with alternating labyrinths. There exist also non-alternating labyrinths. Only among the alternating labyrinths there is exactly one type of labyrinth for each level sequence. The other way round, this allows us to unequivocally describe each type of an alternating labyrinth by its level sequence.

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