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Posts Tagged ‘Cretan labyrinth’

The silver coins of Knossos are quoted again and again when we talk about the labyrinth. They can be found in the major museums of the world.

Last year I was able to see and photograph one of them on a trip to Vienna in the Coin Cabinet of the Kunsthistorisches Museum.

Kinsthistorisches Museum Wien

Kinsthistorisches Museum Wien

The book “Labyrinths” by Hermann Kern shows illustrations of 20 coins from the British Museum in London.

Meanwhile there is a digital interactive catalog of the Coin Cabinet of the Staatliche Museen zu Berlinn, where you can access more than 34,000 coins.

With the search term “Labyrinth Knossos” I found 22, which I can show here under the following license.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Germany License.

The coins cover a period of 425 BC until 12 BC. Shown is mostly the reverse of the coin.

For the interpretation of the representations I have found some interesting information in the description that I quote here (translated from German):

The Cretan town of Knossos has been closely linked to the myth of the Minotaur since antiquity. His mythical dwelling, the labyrinth, was one of the city’s landmarks. However, the depiction of the labyrinth on the Knossos coins came in very different ways, since a real non-existing place had to be shown. The labyrinth is always pictured in supervision, but with different outer shapes and structuring. Only in supervision, the labyrinth can be detected as such.

I highly recommend visiting the digital catalog. There are to find many additional details about the coins. In particular, there is the possibility to look at both sides and to retrieve further information.

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Quite simply: By leaving off the barriers in the minor axes. I have already tried this with the Chartres labyrinth (see related posts below). But is that also possible with every other Medieval labyrinth?

As an example I have chosen the type Auxerre that Andreas showed here recently. This labyrinth is self dual as are Chartres and Reims, therefore of special quality. And they all have a complementary version.

The Auxerre labyrinth

The Auxerre labyrinth

Here the original with all the lines and the path in the labyrinth, Ariadne’s thread. The barriers in the minor axes are identical with those of the Chartres type. There is only another arrangement of the turning points (the lanes 4, 5, 7, 8) in the middle of the main axis.

The original Auxerre labyrinth without the barriers

The original Auxerre labyrinth without the barriers

The barriers are omitted. When drawing Ariadne’s thread, I found that four tracks could not be inserted. Hence, I have anew numbered the circuits and there remain now 7 circuits instead of the original 11. However, this also means that by changing this Medieval labyrinth into a concentric Classical labyrinth through this method no 11 circuit labyrinth is generated, but a 7 circuit.

The 7 circuit circular Cretan labyrinth

The 7 circuit circular Cretan labyrinth

If one looks more exactly at it, one recognises the well-known path sequence: 3-2-1-4-7-6-5-8. We got a Cretan labyrinth in concentric style.


Now we turn to the complementary labyrinth:

The complementary Auxerre labyrinth

The complementary Auxerre labyrinth

The complementary labyrinth is generated by mirroring the original one. The upper barriers remain, right and left they run differently and in the main axis, the turning points shift. The entrance into the labyrinth changes to the middle (lane 9) and the entrance into the center is from further out (lane 3).

The complementary Auxerre labyrinth without the barriers

The complementary Auxerre labyrinth without the barriers

As with the original, four lanes can not be inserted (4, 5, 7, 8). Therefore, the result is again a 7 circuit labyrinth. I renumbered the lanes and have redrawn the labyrinth.

This is how it now looks like:

The complementary 7 circuit circular Cretan labyrinth

The complementary 7 circuit circular Cretan labyrinth

The labyrinth is entered on the 5th lane, the center is reached from the 3rd lane. The path sequence is: 5-6-7-4-1-2-3-8. This labyrinth is not one of the historically known labyrinths. But it showed up in this blog several times (see related posts below). Because it belongs to the interesting labyrinths among the mathematically possible 7 circuit labyrinths.

The surprising fact is that no 11 circuit Classical labyrinth could be generated through the transformation. But for that  the 7 circuit Cretan labyrinth. Therefore we can say that the heart of the Medieval Auxerre labyrinth is the Cretan (Minoan) labyrinth as it is in the Chartres labyrinth.

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Andreas recently brought here a posting to the Jericho labyrinth St. Gallen which probably shows the historically first crossing of the main axis in a classical labyrinth.

I have written about that already. But now I would like to do it once again. Because for me it seems to be an element to design the labyrinth which I have not seen anywhere.

I became aware of that when I have no longer drawn the labyrinth from a seed pattern, but from the path sequence. And, besides, have noted that there also are different possibilities to connect the lines.

Using the example of the classical 7 circuit labyrinth I will explain this once again. How many possibilities to cross the axis are there, and how does it look like?

First the original labyrinth, however round and with a bigger middle.

The classical 7 circuit labyrinth

The classical 7 circuit Labyrinth

The last path sequence into the middle lies on the vertical main axis. The entrance lies on the left side of the main axis, leads to the third circuit, and turns to the left at first. The entry into the middle takes place from the fifth circuit from the right side, and faces the entrance.


How often can I now traverse the axis?
At two positions: From the first to the fourth circuit, and from the fourth to the seventh circuit. This can happen at each position alone or at both positions together. The result are three variations.

Here the first version:

Crossing the axis from the 1st to the 4th circuit

Crossing the axis from the 1st to the 4th circuit

By crossing the main axis from the first to the fourth circuit I do not change the direction of movement as in the original labyrinth. I am still turning to the left in the fourth circuit.
However, thereby I also reach the middle from the left side, so to speak I have laid this entry on the other side of the main axis.
The main entrance slides a little further to the left, and the two lower turning points also move to the left.


The second version:

Crossing the axis from the fourth to the seventh circuit

Crossing the axis from the fourth to the seventh circuit

Here the change from the first to the fourth circuit remains like in the original, however, from the fourth to the seventh circuit I maintain the “spin”.
The entry into the middle is executed from the left side as it is in the original. However, the main entrance slides to the right side. Both lower turning points are shifted to the right.


The third version:

Crossing the axis from the first to the fourth, and from the fourth to the seventh circuit

Crossing the axis from the first to the fourth, and from the fourth to the seventh circuit

The vertical main axis is crossed twice as in the previous versions, now together.
Through that the  lines are displaced considerably. Everything moves to the left. The main entrance lies again on the left side, the entry into the middle is made from the right side.


Here the path as Ariadne’s thread:

Ariadne's thread in familiar manner

Ariadne’s thread in familiar manner

Ariadne's thread with the axis crossed twice

Ariadne’s thread with the axis crossed twice

 

 

 

 

 

 

 

 

 

 

Maybe one can dismiss that as unnecessary? It would be nice, nevertheless to try it out in practice. Above all how it feels to experience another change of direction than in the original.

Maybe the opportunity arises in a big sandtable exercise? On a sandy beach for example? Where one can simply scratch the lines into the sand, and allows the flood to erase them out leniently.

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The oldest known labyrinth figure is the Classical 7 Circuit labyrinth (sometimes also called: the Cretan labyrinth). Its origin is about 1200 B.C. The further development falls in the time of the Roman empire from 165 B.C. till 400 A.D. The general name is Roman labyrinth and there are different types again. They have in common that different sectors (mostly four) are run one after the other.

The Classical 7 circuit labyrinth in square form

The Classical 7 circuit labyrinth in square form

In his book “Labyrinths and Mazes of the World” (published in 2003 by Gaia Books, London) Jeff Saward has described how the development of the Roman labyrinth from the Classical labyrinth is possible. Her I only want to put this across in a few steps.

We begin with the Classical labyrinth in square form.
In the drawings the boundary lines are shown in black. The seed pattern contained therein is emphasized in blue. The ways are put in orange, in the same width as the boundary lines.

The whole figure is reduced to a quarter through a rotation. The vertical parts of half the seed pattern move to a horizontal line.

The quartered Classical labyrinth

The quartered Classical labyrinth

To generate an entire Roman labyrinth from the quartered labyrinth, another two circuits must be inserted in every sector: One around the middle, and one at the outside. In the outer rings one walks to the the next sector, the last path leads to the center.
If one examines exactly the paths, one can recognize that the way is the same as the way back in a Classical labyrinth. Or differently expressed: In a Roman labyrinth one wanders four times the way back of a Classical labyrinth.

The Roman labyrinth

The Roman labyrinth

The path sequence can be understood with the help of the figures.  So one well can see the Classical labyrinth inside the Roman labyrinth.

Even better one recognizes the relationship with the Classical labyrinth in the diagram illustration.

The diagram of the Roman labyrinth

The diagram of the Roman labyrinth

The Roman labyrinth is self-dual like it is the Classical labyrinth. One sees this well in the following graphics. Howsoever the diagram is rotated or mirrored, the path sequence is always the same. Also it plays no role whether one walks in direction to the center or reversed, or whether one fancies the entrance below or on top.

The diagram of the Classical labyrinth in four variants

The diagram of the Classical labyrinth in four variants

There are different historical Roman labyrinth of this kind. The oldest one comes from the second century A.D. and is to be seen on a mosaic in Pont Chevron (France). This is why Andreas Frei calls it type Pont Chevron (see link below).

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Many are surprised how long the way in a labyrinth can be, especially if they walking labyrinth for the first time. And many who want to build a labyrinth, e.g., with stones or with candles, are astonished how much material they need.

Under the heading “Principles of Form” in his book Labyrinths Hermann Kern writes about the >tortuous path principle<:

– if the path fills the entire interior space by wending its way in the most circuitous fashion possible

If I stand ahead of a labyrinth, the middle, the goal is within  my reach. However, only when walking in I get to know how winding and complicated the way is in reality. But yet, this way, the red thread or Ariadne’s Thread is the continuous line in the labyrinth, without crossroads or junctions.

Ariadne's Thread

From A to Z: The long and the short path

In the drawing I call “A” the beginning of the path and “Z” the goal, the center or middle. In many labyrinths I could reach directly the middle with a few steps across all limitations. But this is not really what is intended with a labyrinth.

Now I compare for a 7 circuit labyrinth with a diameter of about 15 m the short way (direct connection between A and Z) with the long way along the Ariadne’s Thread. The length of the short way amounts to 6.33 m, the long way has a length of 154.62 m. Or differently expressed: The long way is 24.4 times longer than the short way (154.62: 6.33 = 24.4).
One could also see in this a formula for the labyrinth. To calculate how powerful is the  layout for example. Or how wended is the way? Or from what minimal surface area I can extract which maximal length?
Maybe one could call this value in honour of Hermann Kern “detour factor” 24.4?

If I handle this thread at the beginning and at the end and pull it apart, I will get a straight line which reaches from “A” to” Z” and is as long as the way inside the labyrinth, i.e. 154.62 m.
I can arrange this to a circle. The perimeter corresponds to the straight line of 154.62 m. The resulting diameter would be 49.22 m.
I can also make a square with the same extent from it. Then this would have four side lengths of 38.65 m.

The following drawing, yet not true to scale, illustrates the different figures and the true ratios among each other:

Ariadne's Thread unrolled

Ariadne’s Thread unrolled

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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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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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