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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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Closing

To wrap-up this series I will here summarize the most important findings and also address some open questions. I have distinguished between type and style. I define the types according to the course of the pathway. This can best be seen in the pattern (re. pattern see related posts, below).  I attribute labyrinths with the same course of the pathway to the same type (Type or Style / 6, see related posts).

I refer to style as a trailblazing way of the graphical design of labyrinths. I have first identified five different styles (Type or Style / 7) and then added the Knidos style by Erwin as a sixth style (Type or Style / 8). Type and Style complement each other. Defining the types according to the course of the pathway is clear, transparent and allows an undoubtful attribution of the individual labyrinth examples. If we would use the style a classification of the individual labyrinth examples would be less clear.

The following figures are meant to illustrate the relationship between type and style once more.

The two upper images from the first post (Type or Style / 1) are unusual. They show the two best known types as well as styles. However, they show the types not in their corresponding usual, but in the opposite styles. That is the Cretan type in the Chartres style and the Chartres type in the Classical style. The two lower figures show the types in their corresponding styles, that are familiar to everybody: the Cretan type in the Classical style and the Chartres type in the Chartres style.

A typology according to the course of the pathway is associated with some issues:

A vast number of countless types are thinkable. However, in practice there might exist some hundreds of types of labyrinths. Nonetheless the types must be aggregated further e.g. to sub-groups, groups, families or the like. And this should be done in a clear and comprehensible way.

There are only a few types that occur frequently, i.e. to which a number of various examples are attributed (the Cretan type, type Chartres and a few others). However, there exist many types that are represented by only one example at all. This could be taken in account of in a typology by separating two corresponding groups of types.

There are labyrinth examples in which the pattern may be difficult to obtain. It is therefore also concievable, that labyrinth examples may occur, that cannot be clearly and transparently classified according to the pattern.

So far I have restricted my considerations to unicursal labyrinths. However, an increasing number of labyrinth like figures is arising, that do not adhere to this principle any more. Basically one could create a category for the unicursal types of labyrinths and add other categories for other labyrinth like figures which could then be further subdivided to types.

Giving adequate names to the types is another problem per se. My way to deal with this is to give a type the name of the earliest published example. However I have not consequently adopted this rule. I have left unchanged the names of the most popular types, even if these had not been named after the earliest published example (e.g. Cretan type, type Chartres, type Ravenna, type Saffron Walden). Also this rule is not without problems as not all examples can be sufficiently dated. Furthermore there is always a possibility that an up to now unknown earlier example can be detected.

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A Brief Stylology

In my last two posts I have described six styles.  Of course, these can also be used to order labyrinths. I will show this here in an illustrative manner. I do not take the effort to group all or as many as possible labyrinths into the different styles. I will just use a few examples of each style to illustrate how such a grouping would work.

klassisch

 

Labyrinth Examples in the Classical Style

 

 

konzentrisch

 

Labyrinth Examples in the Concentric Style

 

 

MiM

 

Labyrinth Examples in the Man-in-the-Maze Style

 

chartres

 

Labyrinth Examples in the Chartres Style

 

reims

 

Labyrinth Examples in the Reims or Bastion Style

 

knidos_stil

 

Labyrinth Examples in the Knidos Style

 

Labyrinth Examples in other styles

Of course, with the six styles described above it is not possible to cover the entire spectrum of all labyrinths. Therefore I have added another group to capture other styles and attributed some examples of labyrinths to it. Among the many labyrinths that cannot be attributed to one of the six styles above, it is possible to identify other styles. This particularly applies to labyrinths of which several examples exist in the same style. This, for instance, applies to the last two examples shown in the other styles group (Other 8, Other 9).

We have now ordered the individual labyrinth examples by styles. The result is also a typology or at least an approach to a typology. The only criteriun we have used for the definition of the types is the style. We thus have defined: type = style.

Because style cannot be defined clearly and unambigously, to me it is not well suited as a criterion for the constitution of a typology. Based on style it is not possible to form a complete range of mutually exclusive groups or types of labyrinths. Furthermore, style does not show the essential of a labyrinth.

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What is a Style?

What determines a style cannot be defined as easily and clearly as a type of labyrinth. Style can be described as a trailblazing way of the design of labyrinths. Usually various types of labyrinths can be designed in the same style. And, vice versa, the same type of labyrinth can be realized in various styles.

In the following I will show some styles. Please give attention to the figure and do not care about what is in it. Regarding the style, the numbers of arms, circuits or the level sequence have no importance. These are important for the type. We can also say: The style is not the content but the form. Or more sensually: What’s the wine for the enologist is the type for the labyrinthologist, and similarly the vessel is the style. Therefore I deliberately show the styles using a figure that is no labyrinth in the strict sense. This figure has one entrance and one access to the center, but only one circuit. It can be considered as a predecessor of a labyrinth. This also helps me to show that the style is something truly different, complementary to the type.

The classical style results if we start from a seed pattern and finalize a labyrinth quasi freehand. This results in a particular form of layout. There is no exact definition of this layout. Rather it may vary between almost circular and rectangular according to the drawer or the type of labyrinth shown in this style.

klassisch

Figure 1. The Classical Style

Fig. 1 shows the essential features of this style. The center of the labyrinth is narrow and formed like a dead-end. The circuits on this side and the opposite side of the axis are shifted. Every one-arm labyrinth can be designed in this style; it is even possible to realize labyrinths with multiple arms in the classical Style.

The example in the concentric style shows best which figure I used for the presentation of the various styles.

konzentrisch

Figure 2. The Concentric Style

The essential characteristics of this style are that the middle of the figure and the center of the labyrinth are matching. Also, the center is somewhat enlarged. The axial wall can but does not need to lie on a radius aligned to the center. A point in the center may but does not need to be visible. This style can often be found in labyrinths of manuscripts. In some of them one can see the central point where the compass has been applied.

The Man-in-the-Maze style has already been extensively described on this blog. It is a very good example for what determines a style: This is the original way of a graphical realization – in this case on a strict geometric grid.

MiM

Figure 3. The Man-in-the-Maze Style

Although they lie on a template of concentric circles, the MiM labyrinths are eccentric. In this style, the center of the labyrinth cannot lie in the middle of the figure. The middle of the figure matches with the center of the seed pattern.

Also the extraordinary design of the labyrinth in Chartres cathedral illustrates well what may constitute a style.

chartres

Figure 4. The Chartres Style

What particularly characterizes this style are the lunettes in the center and the lunations at the exterior of this labyrinth. Several labyrinth examples exist that adapted the Chartres style either in the use of the lunettes or the lunations or both elements of this style together. So, Chartres is also a style! We therefore have to deal with a Chartres type and a Chartres Style. We will have to come back to this later.

The same applies to the labyrinth of Reims too. We could also speak of a Reims style or a Bastion style.

reims

Figure 5. The Reims Style

The labyrinth that has been laid out in the Reims cathedral also has a pioneering design. I do not primarily mean the lawful proportions and composition of the octagonal forms. This per se also deserves attention. However, what constitutes the Style is the bastions. Such bastions, also with varied, rounded shapes, have been adapted in many other labyrinths.

Many other labyrinth examples have special graphical features, e.g. Nîmes, Ravenna, Al Qazwini, Cakra-vyuh. Some of these are singular examples. What constitutes a style cannot be conclusively resolved. Which element may characterize a style, and whether only one or multiple elements be required to characterize a style will be controversial. However, what seems a central requirement to me is that a style can be found in various examples of labyrinths. So that it has influenced other labyrinths.

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At the moment I am occupied a little more intensely with the Chartres labyrinth. Thereby I have discovered anew the photos which I have already taken in 2003 and 2004 at Chartres. Every picture is also to be seen somewhere on mymaze.de. But here on the blog there are quite different possibilities of representation. So I show once again a small choice in a slide show.

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In the meantime, I have already seen several Chartres labyrinths in paved form or slab-lined. But none could persuade me properly. Hence, I have considered how one could build a Chartres labyrinth as a stone labyrinth and what should be taken into account. Thus I developed this layout.

First a look at the original, shown in a self-sketched drawing:

The Chartres labyrinth

The Chartres labyrinth

This labyrinth is considered by many labyrinth enthusiasts worldwide to be the most beautiful and perfect one. It is really unique and has some particularities: The alignement, the middle with the six petals, the lunations, the proportions of the single elements and most notably the quality of execution. It was built shortly after 1200 and presumably at the same time with the remaining floor in the cathedral of Chartres. It is a inherent part of a Gothic church.
Some believe that one might recreate a Chartres labyrinth only 1:1, so in the original dimensions and in the same form.
If I want to build a Chartres labyrinth outside and in the today’s time and with the building materials available today, I do not need, in my opinion, to keep slavishly to the original. But I should pay attention to the basic facts.
These would be for me: The correct alignment of the axes, the proper sequence of lines, a uniform path width, approximately the same proportions as the original. These are, e.g., 1:4 for the relation of wall width to path width or that the middle is one quarter of the whole diameter.
In the original the path is on average 34.4 cm wide with a limitation wall of about 8.2 cm (dimension between axes therefore 42.6 cm). In a confined space this is just acceptable. But inside an open-air labyrinth the way should be broader a little. There are 40 – 50 cm possibly the minimum. Hence, one must not necessarily observe the original measurements. 
On an implementation with paving-stones the passages of the arch-shaped and radial stones at the narrow turning points are especially important. Here the exact position and the direction of the joints is very important.
The middle can be built with the six petals, however, could be also simply empty.
To my opinion the lunations are not absolutely necessary, because the sense and purpose of the same is not clear. They possibly are simply anchorage stones or transition elements in the floor of the cathedral.

A paved 11-circuit medieval labyrinth

A paved 11-circuit medieval labyrinth

The draft is a sort of system drawing which can be scaled just as one likes. The relation of path limitation (20 cm) to road width (80 cm) is 1:4 and therefore results a dimension between axes of 1 m. Besides, the whole diameter would be 29.40 m at a middle of 7.40 m and a path length of 626.18 m. Through a reduction by the factor 0.5 one would have 14.70 m for the diameter and a path length of 313.09 m.

Here in detail how the middle could be made:

Details of the centre

Details of the centre

Here you can see, print or copy the design drawing for a paved 11-circuit labyrinth in Chartres style with the essential measurements as a PDF file.

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