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In Greek mythology, the labyrinth is the place where the Minotaur is hidden and imprisoned. It is therefore not necessarily a real place.
The labyrinth, as we know it today, is highly inappropriate. Because it has an entrance, a clear path and an accessible center.
Thus, on the silver coins from Knossos we also find very different interpretations of the labyrinth. There are meanders and other symbolic representations.
I want to pick out a motif today and take a closer look at it.

I found two examples with the same motif. One on a coin from the Coin Cabinet of Berlin:

Minotaur 420-380 BC

Minotaur 420-380 BC: Coin Cabinet of the Staatliche Museen zu Berlin, object 18218282 obverse

Labyrinth 420-380 BC.

Labyrinth 420-380 BC: Coin Cabinet of the Staatliche Museen zu Berlin, object 18218282 reverse

And one on a coin from the British Museum in London:

Square area meander 500-431 BC

Square area meander 500-431 BC / source: Hermann Kern, Labyrinthe (German edition), 1982, fig. 43

They both represent the same thing. Although the “Berlin” coin seems to be more exact, it contains small errors in two places in the upper area. Two vertical lines collide, where a gap should actually be. This area is more accurately represented on the “London” coin, although the lines there are harder to see.

I made a “final drawing” that shows what the coin maker wanted to show. You can see lines that follow a certain pattern. They are symmetrical, repeating themselves and showing an intricate “path system”. The drawn red thread shows that.
There are four nested paths without beginning and end, but also without entrance. This is not “our” labyrinth but better suited as a prison. The Minotaur would not come out that fast.

The revised area meander

The revised area meander

This could be a hint of the Roman sector labyrinth hundreds of years later.

But it also shows a certain relationship to the Babylonian labyrinth, hundreds of years older and developed in a different culture (see the labyrinthine finger exercises in the post about the Babylonian labyrinth).

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Sector Labyrinths

At the end I will also transform a sector labyrinth into the MiM-style. What is special in sector labyrinths is, that the pathway always completes a sector first, before it changes to the next. As a consequence of this, the pathway only traverses each side-arm once. Thus it seems, that sector labyrinths may be easier transformed into the MiM-style than other labyrinths with multiple arms. I will use as an example a smaller labyrinth with four arms and five circuits. There exist several labyrinth examples of this type. I have named it after the earliest known historical example, the polychrome mosaic labyrinth that is part of a larger mosaic from Avenches, canton Vaud in Switzerland.

Figure 1. Sector Labyrinth (Mosaic) of Avenches

Figure 1 shows the original of this labyrinth (source: Kern 2000: fig 120, p 88). It is one of the rarer labyrinths that rotate anti-clockwise. On each side of the side-arms it has two nested turns of the pathway and 3 nested turns on each side of the main axis. The pattern corresponds with four double-spiral-like meanders arranged one after another – Erwin’s type 6 meanders (see related posts 2). When traversing from one to the next sector the pathway comes on the outermost circuit to a side-arm, traverses this on full length from outside to inside and continues on the innermost circuit in the next sector.

In order to bring this labyrinth into the MiM-style, first the origninal was mentally rotated so that the entrance is at bottom and horizontally mirrored. By this it presents itself in the basic form, I always use for reasons of comparability. Fig. 2 shows the MiM-auxiliary figure.

Figure 2. Auxiliary Figure

This has 42 spokes and 11 rings what makes it significantly smaller than the ones for the Chartres, Reims, or Auxerre type labyrinths. The number of spokes is determined by the 12 ends of the seed pattern of the main axis and the 10 ends of each seed pattern of a side-arm.

In fig. 3 the auxiliary figure together with the complete seed pattern including the pieces of the path that traverse the axes is shown and the number of rings needed is explained. For this the same color code as in the previous post (related posts 1) was used.

Figure 3. Auxiliary Figure, Seed Pattern and Number of Rings

As here the angles between the spokes are sufficiently wide, it is possible to use all rings of the auxiliary figure for the design of the labyrinth. We thus need no (green) ring to enlarge the center. Only one (red) ring is needed for the pieces of the path that traverse the axes – more precisely: for the inner wall delimiting them –, four (blue) rings are needed for the three nested turns of the seed pattern of the main axis, one ring (grey) for the center, and five rings (white) for the circuits, adding up to a total of 11 rings.

Fig. 4 finally shows the labyrinth of the Avenches type in the MiM-style.

Figure 4. Labyrinth of the Avenches Type in the MiM-Style

The figure is significantly smaller and easier understandable than the labyrinths with multiple arms previously shown in the MiM-style. Overall it seems well balanced, but also contains a stronger moment of a clockwise rotation that is generated by the three asymmetric pieces of the pathway and of the inner walls delimiting these on the innermost auxiliary circle.

Related posts

  1. How to Draw a MiM-Labyrinth / 14
  2. How to Find the True Meander for a Labyrinth

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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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Labyrinths With Multiple Arms

Until now, almost exclusively labyrinths of the basic type (Cretan type) have been implemented in the Man-in-the-Maze style. All one-arm labyrinths can be drawn in this style (see related posts 2, below). But is this also possible in labyrinths with multiple arms? I have tried this out with the most famous labyrinth with multiple arms, the Chartres type labyrinth. And it works. I have already shown the result in January (see related posts 1). In order to arrive there, a prolonged process was needed. In the following I will describe the detailed steps.

Jacques Hébert† has shown on his website (see further links 1, below), that a one-arm labyrinth exists, which has the same seed pattern as the main axis of the Chartres type labyrinth. He had derived this from the enigmatic labyrinth drawing (fig. 1) contained in a medieval manuscript.

Figure 1. Enigmatic Labyrinth Drawing from a Manuscript Compiled 860-862 by Heiric of Auxerre

For this, he had deleted the hand drawn figures indicating the side-arms and closed the gaps where the walls delimiting the pathway were left interrupted. He had named the labyrinth after learned Benedictine monk Heiric of Auxerre who had compiled this manuscript in about 860 – 862.

Figure 2. Labyrinth Named after Heiric of Auxerre by Jacques Hébert

The website of Hébert is no longer active any more. Thanks to a note by Samuel Verbiese we can now find it again in The Internet Archive (see further links 2). Erwin also has introduced this type of labyrinth in this blog (see related posts 3).

The Heiric of Auxerre labyrinth is ideally suited as a starting point. It is quasi the Chartres type as a one-arm labyrinth. So let us first transform this labyrinth into the MiM-style (fig. 3).

Figure 3. The Heiric of Auxerre Labyrinth in the MiM Style

The seed pattern of this labyrinth has 24 ends as have all seed patterns of labyrinths with 11 circuits. So we need an auxiliary figure with 24 spokes for the transformation into the MiM-style.

Next, the side-arms have to be included. A first attempt can be made by retrieving the barriers. This can be achieved by inserting 3 additional spokes for each side-arm as shown in fig. 4.

Figure 4. Insertion of the Side Arms

Thus, the auxiliary figure is extended from 24 to 33 spokes. The result is shown in fig. 5.

Figure 5. Labyrinth of the Chartres Type…

This now looks quite decently like a MiM labyrinth. However, upon a closer view it reveals as unsatisfactory. Fig. 6 shows the reasons why.

Figure 6. … in a Hybrid Style

This labyrinth is of a hybrid style. While the main axis is formed in the MiM-style, the side-arms, however, are in the concentric style. The turning points of the pathway (red arcs in the figure) on the main axis are aligned along the circles of the auxiliary figure. On the side-arms, however, they are aligned along the spokes. What is characteristic for the MiM-style is the seed pattern of the main axis. The figure looks much like a labyrinth in the MiM-style because the main axis with it’s 24 of 33 spokes dominates the whole picture.

Therefore, if we want to implement a labyrinth with multiple arms in the MiM-style, we must also transform the side-arms into the MiM-style. For this it is necessary to really understand and consequently adopt

  • how the seed pattern is organised in the MiM-style
  • and correspondingly, how the pieces of the pathway traversing the arms have to be designed.

More about this in following posts.

Related posts:

  1. Our Best Wishes for 2018
  2. How to Draw a Man-in-the-Maze Labyrinth
  3. Does the Chartres Labyrinth hide a Troy Town….

Further Links:

  1. Website by Jacques Hébert
  2. The Internet Archive

 

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In addition to the universally known labyrinth of Chartres and the less popular labyrinth of Reims a third, much less known, very interesting (interesting and self-dual) medieval labyrinth with 4 arms and 11 circuits has been preserved. This is sourced from a manuscript that is stored in the municipal library of Auxerre. Therefore I have named it as Type Auxerre.

At the end of this series I want to show these three labyrinths and their complementaries.

In the three following figures I start with the original labyrinth (image on top left).

From this I obtain the pattern by unrolling the Ariadne’s Thread of it (image on top right).

Then I mirror the pattern vertically without interrupting the connections to the exterior and to the center. This results in the pattern of the complementary labyrinth (image on bottom right).

Then I curl in this pattern to obtain the complementary labyrinth (image on bottom left).

Fig. 1 shows this procedure with the example of the labyrinth of Auxerre. This labyrinth is not recorded in Kern [1]. The image of the original labyrinth was taken from Saward [2] who sourced it from Wright [3].

Figure 1. Labyrinth of Auxerre and Complementary

Fig. 2 shows the labyrinth of Reims and the complementary of it. The image of the original labyrinth was sourced from Kern [1].

Figure 2. Labyrinth of Reims and Complementary

Finally, the labyrinth of Chartres and it’s complementary are presented in fig. 3. The image of the original labyrinth was sourced from Kern [1].

Figure 3. Labyrinth of Chartres and Complementary

With these considerations I wanted to point out that three historical labyrinths exist with a similar degree of perfection as Chartres. Together with their complementaries we now have present six very interesting labyrinths with 4 arms, 11 circuits and a similar degree of perfection.

[1] Kern, H. Through the Labyrinth. Prestel, Munich 2000.
[2] Saward J. Labyrinths and Mazes. Gaia, London 2003.
[3] Wright C. The Maze and the Warrior. Harvard University Press, Cambridge (Massachusetts) 2001.

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Just like the labyrinth from Ravenna, the Wayland’s House labyrinth is also a historical type of labyrinth with 4 arms and 7 circuits. There exist even two different Wayland’s House labyrinths (figure 1).

Figure 1. The Two Wayland’s House Labyrinths

 

I have named them as Wayland’s House 1 and Wayland’s House 2. Wayland’s House 1 first appeared in a manuscript of the 14th century, Wayland’s House 2 in a manuscript of the 15th century, both from Iceland. This can be easily looked up in Kern. In the following I refer to Wayland’s House 1.

In this type of labyrinth, the pathway does not enter on the first circuit and does not reach the center from the last circuit either. Therefore it is an interesting labyrinth. And also the complementary of it is an interesting labyrinth. This, however, is not the most important reason for why I present this type of labyrinth and its’ relatives here. Whereas no existing examples of any relative of the Ravenna labyrinth are known, there exists a contemporary type of labyrinth for each, the dual, complementary and complementary-dual of the Wayland’s House labyrinth.

Figure 2 shows the patterns of the original Wayland’s House labyrinth (a), the dual (b), complementary (c) and complementary-dual (d) labyrinths.

Figure 2. The Relatives of the Wayland’s House Type – Patterns

The original (a) and dual (b) both are interesting labyrinths. The complementaries of them, (c) and (d), are likewise interesting labyrinths.

Figure 3 shows the labyrinths corresponding to the patterns in their basic form with the walls delimiting the pathway shown on concentric layout and in clockwise rotation.

Figure 3. The Relatives of the Wayland’s House Type – Basic Forms

The relatives of the Wayland’s House type (a) are three of the so-called neo-medieval labyirnth types (there are other neo-medieval types of labyrinths too). These relatives are: dual (b) = „Petit Chartres“, complementary (c) = „Santa Rosa“, and complementary-dual (d) = „World Peace“ labyrinth.

So these contemporary types of labyrinths can be easily generated simply by rotating or mirroring of the pattern of Wayland’s House. This having stated I do not mean to pretend, these types of labyrinths have intentionally or knowingly been derived in such a way from the Wayland’s House type. Rather, available information suggests that they were created in a naive way, i.e without their designers having known about this relationship with the Wayland’s House type labyrinth. Nevertheless, actually, these modern neo-medieval labyrinths are the relatives of Wayland’s House.

The Wayland’s House labyrinth at first glance has some similarities with the Chartres type labyrinth. However it is not self dual and its course of the pathway is guided by an other principle yet. And this applies to its relatives too. Therefore the choice of the name „Petit Chartres“ to me seems inconvenient. It seems like this name was chosen because this type of labyrinth originally was designed in the Chartres-style. So this type seems to have been named after its style.

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Among labyrinths with mulitple arms it is also common that one labyrinth is interesting and the complementary to it is uninteresting. An example for this is the labyrinth of the type Ravenna (figure 1).

Figure 1. The Labyrinth of Ravenna

This labyrinth has 4 arms and 7 circuits. The pathway enters it on the innermost circuit and reaches the center from the fifth circuit. It is, thus, an interesting labyrinth. This type of labyrinth has been named after the example laid in church San Vitale from Ravenna. What is really special in this example is the graphical design of the pathway. This is designed by a sequence of triangles pointing outwards. The effect is, that the direction from the inside out is strongly highlighted. This stands in contrast to the common way we use to approach a labyrinth and seems just an invitation to look up the dual of this labyrinth. Because the course of the pathway from the inside out of an original labyrinth is the same as the course from the outside into the dual labyrinth.

I term as relatives of an original labyrinth the dual, complementary, and complementary-dual labyrinths of it. In fig. 2 the patterns of the Ravenna-type labyrinth (a, original), the dual (b), the complementary (c), and the complementary-dual (d) of it are presented.

Figure 2. The Relatives of the Ravenna-type Labyrinth – Patterns

The original (a) and the dual (b) are interesting labyrinths. The complementaries of them are uninteresting labyrinths, because in these the pathway enters the labyrinth on the outermost circuit (c) or reaches the center from the innermost circuit (d). The dual of an interesting labyrinth always is an interesting labyrinth too, the dual of an unintersting is always uninteresting labyrinth too.

Figure 3 shows the labyrinths corresponding to the patterns in their basic form with the walls delimiting the pathway on concentric layout and in clockwise rotation. Presently, I am not aware of any existing examples of a dual (b), complementary (c) or complementary-dual (d) to the Ravenna type labyrinth (a).

Figure 3. The Relatives of the Ravenna-type Labyrinth – Basic Forms

From these basic forms it can be well seen that it seems justified to classify the complementary and complementary-dual labyrinths as uninteresting. The outermost (labyrinth c) and innermost (labyrinth d) respectively walls delimiting the path appear disrupted. Therefore labyrinths c and d seem less perfect than the original (a) and dual (b) labyrinths, where the pathway enters the labyrinth and reaches the center axially.

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