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Posts Tagged ‘type’

The Labyrinth on Folio 51 r

In the previous post I have presented the nine labyrinth designs by Gossembrot and gave references to the sources (see below: related posts 1). The first labyrinth on folio 51 r undoubtedly is the most important of all. It is the earliest preserved example of a five-arm labyrinth at all. Furthermore, it’s course of the pathway is unprecedented and deviates from every previous type of labyrinth. Here I will show the course of the pathway and it’s special features stage by stage. For this, I use the Ariadne’s Thread inscribed into the labyrinth and in parallel the pattern. This is the same approach I had applied with the labyrinth by Al Qazvini (related posts 2). As a baseline I always use a labyrinth with the entrance on bottom and in clockwise rotational direction. Gossembrot labyrinth fol. 51 r, however, rotates anti-clockwise. Therfore, in figure 1, I first mirror the labyrinth horizontally.

Figure 1. Labyrinth on Folio 51 r (left), horizontally mirrored (right)

The image on left shows the original labyrinth of fol. 51 r, the right image shows the same labyrinth mirrored. Mirroring does not affect the course of the pathway with the exception of the pathway traversing in the opposite direction.

Fig. 2 shows the first stage of the course when it enters the labyrinth. This is nothing special. The path fills the space left over by the pattern and continues to the innermost circuit as directly as possible.

Figure 2. Way into the Labyrinth

This circuit is then traversed in a forward direction through all five segments, as can be seen in fig. 3. This is also nothing special either.

Figure 3. Forward Direction on the 7th Circuit Through all Segments

The special characteristic of the course of the path starts after it has turned at the end of the fifth segment. Then it proceeds to a movement in backward direction, following a line that alternates between forming a curve wrapping and being wrapped and also marking the axes. This process continues to the first side-arm (fig 4).

Figure 4. Backward Direction Onset of Special Course

At this point the former course is interrupted. Again the path marks the axis (first side-arm), but then continues as a meander through segment 2, as shown in fig. 5.

Figure 5. Backward Direction, Interruption, Insertion of Meander

From there the original course is resumed. Still in a backward direction, the pathway fills the rest of segment 2 and segment 1 and finally turns from the 2nd to the 1st circuit (fig. 6).

Figure 6. Backward Direction, Resumption of Special Course

From here now it continues again in forward direction and takes it’s course through all segments until it reaches the opposite side of the main axis. In passing, it fills the inner space it had left over on its course in backward direction in segments 3 and 4 (fig. 7).

Figure 7. Forward Direction Through all Segments

From there it reaches the center after having filled the space left over in segment 5 (fig. 8).

Figure 8. Completion, Reaching the Center

This course of the pathway, like in some sector labyrinths, results in symmetric pairs of nested turns of the pathway at each side-arm. Unlike in sector labyrinths, however, the pathway does not complete one sector after another, but traverses through all sectors in each direction. First in forward direction on the innermost circuit, then in backward direction modulating through circuits 6 to 2, and finally again in forward direction on circuits 1, 4, and 5.

Related Posts:

  1. Sigmund Gossembrot / 1
  2. The Labyrinth by Al Qazvini

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Type and Style

In my post Type or Style / 4 from August 2015, I have discussed the typology of the website Begehbare Labyrinthe (related posts 4). In the meantime, this typology has been completely revised (additional links). The new typology adopts our principles relating to type (related posts 3) and style (related posts 2). Furthermore it combines type and style. All walkable labyrinths were now attributed to types according to their course of the pathway. Labyrinths with the same course of the pathway (pattern, sequence of circuit) are of the same type. These types were then further divided into groups according to the style. Also the naming of the types has been reworked.

This whole thing can be well explained using the basic type. „Basic type“ is the new name of the type that formerly or elsewhere has been termed „classical“ or „Cretan“ type of labyrinth. This type has one axis, seven circuits and the pattern shown in fig. 1.

Figure 1. Pattern Basic Type

Figure 1 shows the pattern in pure form on left, and on right with an aid how to read it. It is read from top left to bottom right (related posts 5). To this corresponds the course of the path in it’s sequence of circuits 3 2 1 4 7 6 5 (related posts 1). By this, the type is accurately described. It is the most frequent type of labyrinth worldwide. And also in the typology of Begehbare Labyrinthe it is by far the most frequent type. Means that of the currently included 305 walkable labyrinths, 133 are of the basic type. These are designed in various styles:

  • „triangle“ (1 example)
  • „rectangle“ (1 example)
  • „classic“ (97 examples)
  • „Knidos“ (15 examples)
  • „concentric“ (15 examples)
  • „Man-in-the-Maze“ (1 example)
  • „other“ (3 examples).

Each type of a labyrinth in each of its styles is depicted with a figure of one corresponding labyrinth example. Figure 2 shows as an example the section representing the basic type in the classical style with its 97 examples.

Figure 2. Section Basic Type in Classical Style

If you move the cursor over the image of the labyrinth, the pattern is overlaid. At the side of the image all attributed walkable labyrinths are listed. Moving the cursor over a name makes an image of the corresponding labyrinth fade in. A click into a link brings you to the page with the full entry of the corresponding labyrinth. This often includes a comprehensive image of the whole labyrinth, and an extensive description of it including type, style, number of circuits, number of axes, size and measurements, materials and other information.

At present, the typology includes about 60 different types and some 10 styles. However, not every type is represented in each style. Despite this, the typology at the moment contains 92 groups composed of types and styles, what is more than the 60 pure types, that are based exclusively on the course of the pathway. These groups cover all walkable labyrinths listed in the website. However, from time to time, new labyrinth examples are added and therefore also the number of types and styles may increase further.

The full list of the types of labyrinths is ordered in increasing order first by the number of axes, then by the number of circuits. So, first all one-arm types of labyrinths are listed, and these in ascending order by the number of circuits from the smallest with 3 circuits to the largest with 11 circuits. Next follow the types with 2, 3, 4, 5, 6 und 8 arms, each again in ascending order by the number of circuits.

This new typology is now systematic, consistent, clearly reproducable, and completely covers the listed walkable labrinths. Furthermore it can be easily extended if labyrinth examples in new types or styles are added to the list.

Related Posts:

  1. The Level Sequence in One-arm Labyrinths
  2. Type or Style / 7
  3. Type or Style / 6
  4. Type or Style / 4
  5. How to Read the Pattern

Additional Links:

  1. Typology Begehbare Labyrinthe

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In the last post I have presented four variants of the seed pattern of the Cakra Vyuh type labyrinth. Perhaps somebody might be interested, how the matching complete labyrinths look like. Here I will show them.

I thus add three other examples to the only example (Original) of this type of labyrinth that has been well known until now. Or, more exactly, only two of them are really new: the examples in the Classical and in the Concentric styles. I had already published the example in the Man-in-the-Maze style previously on this blog. Furthermore it has to be considered, that the original labyrinth rotates anti-clockwise. I have horizontally mirrored the three other examples. It is still the same labyrinth then, although rotating clockwise. I use to show all my labyrinth examples in clockwise rotation so they are more easily comparable.

Related Posts:

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A very beautiful labyrinth example (fig. 1) named Cakra-vyuh can be found in Kern’s Book° (fig. 631, p. 294).

Andere 5

Figure 1: Cakra-Vyuh Labyrinth from an Indian Book of Rituals

The figure originates from a contemporary Indian book of rituals. In this, a custom of unknown age, still in practice today, was described, in which the idea of a labyrinth is used to magically facilitate birth-giving. To Kern this is a modified Cretan type labyrinth. I attribute it to a type of it’s own and name it after Kern’s denomination type Cakra-Vyuh (see Related Posts: Type or Style / 14).

The seed pattern is clearly recognizable. One can well figure out that this labyrinth was constructed based on the seed pattern. Despite this, I hesitate to attribute it to the Classical style. For this, the calligraphic looking design deviates too much from the traditional Classical style. The walls delimiting the pathway all lie to a mayor extent, i.e. with about 3/4 of their circumference on a grid of concentric circles. Therefore it has also elements of the concentric style. The labyrinth even somewhat reminds me of the Knidos style with its seamlessly fitting segments of arcs where the walls delimiting the path deviate from the circles and connect to the seed pattern.

Therefore I have not attributed this labyrinth to any one of the known styles, but grouped it to other labyrinths (Type or Style /9). However, I had also drawn this labyrinth type in the Man-in-the-Maze style already (How to Draw a Man-in-the-Maze Labyrinth / 5).

SPCV

Figure 2: Composition of the Seed Pattern

Fig. 2 shows how the seed pattern is made-up. We begin with a central cross. Tho the arms of this cross are then attached half circles (2nd image). Next, four similar half circles are fitted into the remaining spaces in between. Thus the seed pattern includes now 8 half circles (3rd image). Finally, a bullet point is placed into the center of each half circle. We now have a seed pattern with 24 ends, that all lie on a circle.

In the pattern it can be clearly seen, that the labyrinth has an own course of the pathway. Therefore, to me it is a type of it’s own.

Typ Cakra Vyuh

Figure 3: Pattern

Furthermore it is a self-dual, even though, according to Tony Phillips, uninteresting labyrinth (Un- / interesting Labyrinths). This because it is made-up of a very interesting labyrinth with 9 circuits with one additional, trivial circuit on both, the inside and the outside.

Related posts:

 

°Kern, Hermann. Through the Labyrinth – Designs and Meanings over 5000 Years. Munich: Prestel 2000.

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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.

Related posts:

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Once more: Type in Style

I have now needed three posts to attribute all labyrinth examples of this series to their types. Here I present the last part.

 


Examples in the Reims style

Reims 1

Reims 1

 

 

 

Type Reims


Reims 2

Reims 2

 

 

 

Type Reims


Reims 3

Reims 3

 

 

 

Type Chartres


Reims 4

Reims 4

 

 

 

Type Sneinton (labyrinth drawn faultily)


Reims 5

Reims 5

 

 

 

Type Saffron Walden (labyrinth drawn faultily)


Exemples in the Knidos Style

Knidos 1

Knidos 1

 

 

 

Type Knossos


Knidos 2

Knidos 2

 

 

Core-labyrinth of the type Rockcliffe Marsh, doublespiral-like mander (Erwin’s type 6 meander)


Knidos 3

Knidos 3

 

 

 

 

Cretan type


Knidos 4

Knidos 4

 

 

 

 

Type Otfrid


Other Examples

Andere 1

Other 1

 

 

 

Type Rockcliffe Marsh


Andere 2

Other 2

 

 

 

 

Cretan Type


Andere 3

Other 3

 

 

 

 

Cretan Type


Andere 4

Other 4

 

 

 

 

Type Al Qazwini


Andere 5

Other 5

 

 

 

Type Cakra Vyuh


Andere 6

Other 6

 

 

 

Type Liger


Andere 7

Other 7

 

 

 

Type Ely


Andere 8

Other 8

 

 

 

Type Kieser


Andere 9

Other 9

 

 

 

 

Type Gent


We can see here a similar result as in the two previous posts. The 18 examples belong to 14 different types.
What can be seen here also is, that in some labyrinths the pattern may be difficult to obtain (type Liger, type Ely, type Kieser, type Gent). I do not explain this further here because this is beyond the space of this post.

The types used

Related posts:

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Type in Style (continued)

Here I will now attribute the labyrinth examples from my post Type or Style / 9 to types of labyrinths. These examples were grouped in styles.

The examples in the classical style

Klassisch 1

Classical 1

 

 

 

Type Löwenstein 3


Klassisch 2

Classical 2

 

 

 

Type Löwenstein 5a


Klassisch 3

Classical 3

 

 

 

Cretan Type


Klassisch 4

Classical 4

 

 

 

 

Type Löwenstein 9b


Klassisch 5

Classical 5

 

 

 

Type Hesselager


Klassisch 6

Classical 6

 

 

 

Type Tibble


The examples in the concentric style

Konzentrisch 1

Concentric 1

 

 

 

 

Cretan Type


Konzentrisch 2

Concentric 2

 

 

 

Type Hesselager


Konzentrisch 3

Concentric 3

 

 

 

 

Type Otfrid


Konzentrisch 4

Concentric 4

 

 

 

 

Type Chartres


Konzentrisch 5

Concentric 5

 

 

 

 

Type Gossembrot 51r


Konzentrisch 6

Concentric 6

 

 

 

Type Münster


The examples in the Man-in-the-Maze style

MiM 1

MiM 1

 

 

 

Cretan Type


MiM 2

MiM 2

 

 

 

 

Type Pima


MiM 3, MiM 4: no true labyrinths


The examples in the Chartres style

Chartres 1

Chartres 1

 

 

 

Type Chartres


Chartres 2

Chartres 2

 

 

 

Type Trinity


Chartres 3

Chartres 3

 

 

 

 

Type St. John


Chartres 4

Chartres 4

 

 

 

 

Type Petit Chartres


Chartres 5: no true labyrinth

 

Chartres 6

Chartres 6

 

 

 

Type Grey’s Court


In order not to overload this post I interrupt here and present the remaining examples in my next post.

Among the examples here, there are also figures, that are no unicursal labyrinths in the strict sense. For reasons of space I do not explain this further here but will come back to it later.

The types used:

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