Feeds:
Posts
Comments

Posts Tagged ‘level sequence’

There is now a new labyrinth at this extraordinary and historically significant place.

In the church Mariä Schutz a labyrinth was built during the three-year period of renovation and rebuilding on the area of the Vogelsburg.
Father Bernhard Stühler, hospital chaplain of the Juliusspital, initiated it. Architect Stephan Tittl from the office SequenzSieben Würzburg made the architectural design of the church and delivered the layout. During the inauguration of the project turned out, that Sr. Hedwig Mayer, prioress of the Augustinusschwestern on the Vogelsburg, always had wished a labyrinth.

The new labyrinth

The new labyrinth

It’s a newly created sector labyrinth with 5 circuits. In the middle is a bowl-shaped pitch circle to divert the direction. The dividing bars form a cross and are arranged symmetrically.
The diameter amounts to 6 m, the middle to 2 m. The ways are 34 cm wide and are marked by a 6 cm wide brass sheet on the terrazzo floor. The way into the center amounts to about 64 m.

One enters the church from the south over an outside stair. On the left hand of the entrance is the labyrinth which is aligned to the west and the east. You enter it from the west, arriving the center, one looks to the east in the direction of the altar and leaves it also again in this direction.

The Oberpflegeamtsdirektor (Chief Administrative Officer) Walter Herbert of the Juliusspitalstiftung (foundation Juliusspital) said on occasion of the inauguration of the altar in May, 2016 to the interior design of the church:

With the elected interior design and with the labyrinth in the ground we would like to offer to every visitor of the Vogelsburg the possibility to find the way to one’s own center, to get back to basics and to find the possibility of steering towards God in the church space.

The segments of the 5 circuits

The segments of the 5 circuits

As Andreas proposed in his last article we can number the 20 segments for the 5 circuits in this 4-armed labyrinth. The sequence of segments can be derived from it for the pathways. Some segments form a connected section which runs through several quadrants. These segments can be marked by brackets. The sequence of segments then looks as follow: 9-5-(1-2-3-4)-8-12-(16-15)-11-(7-6)-10-(14-13) – (17-18-19-20)-21. I write the result a little bit differently than Andreas and still add the center at the end. Inside this labyrinth we have as a specific feature two segments which enclose the full length of a circuit.

Related Post

Further Links (in German)

Advertisements

Read Full Post »

In one-arm labyrinths, each circuit is represented by one number. Therefore it is possible to capture even quite large labyrinths appropriately with the level sequence. In labyrinths with multiple arms, the pathway may repeatedly encounter the same circuit. Various possibilities exist to take account of this in the level sequence. For this, according to the number of arms, the circuits have to be further partitioned to segments. Here I will show a method in which all segments are numbered through.

For this I use an example of a labyrinth that has repeatedly been presented on this blog. It has 3 arms and 3 circuits.

3_gaengig_3_achsig_rund

First, each circuit is partitioned to three segments. One segment corresponds with a unit of the pathway between two arms. Next, the segments have to be numbered through. This can be done in different ways. Here I number them from the outside to the inside and one circuit after each other.

segmente

Now we can track the course of the pathway through the various segments. This results in the sequence of segments encountered by the pathway. In labyrinths with multiple arms the level sequence thus extends to a sequence of segments.

The sequence of segments of this labyrinth is 7 4 1 2 5 8 9 6 3. The length of this sequence of numbers is a result of the number of circuits multiplied with the number of arms. Thus, for a labyrinth with 3 circuits and 3 arms, 9 numbers are required. Whereas in a one-arm labyrinth with 3 circuits only 3 numbers are needed.

However, besides the numbers no other information is needed. The sequence of segments itself determines where the pathway makes a turn or traverses an axis. In one-arm labyrinths this had to be indicated additionally by use of separators.

Related posts:

Read Full Post »

In an earlier post „Type or Style / 6“ (see related posts, below) I had already mentioned the level sequence. And I had stated two reasons for why I do not use it for naming types of labyrinths.

  • Among the one-arm labyrinths only in alternating labyrinths there exists exactly one type of labyrinth for each level sequence. If we also consider non-alternating labyrinths, in which the pathway traverses the axis, there can exist multiple courses of the pathway for the same level sequence.
  • In labyrinths with multiple arms the level sequence may rapidly increase to a length and complexity that is difficult to memorize.

Here I want to address the first issue further. I do this because there is a very simple solution for it. In one-arm labyrinths every circuit is represented by one number. In real practice only few of the larger labyrinths will have more than 15 – 17 circuits. Most one-arm labyrinths have a markedly smaller size. Therefore these labyrinths could be quite simply be named with their level sequence. But there remains the problem with the ambiguity. Erwin had elaborated on it in his post “The Classical 7 Circuit Labyrinth with Crossed Axis“ (see related posts, below). I will illustrate it here and use some figures of Erwin’s post.

uf_3214765

Figure 1. Level Sequence 3 2 1 4 7 6 5

In Figure 1 three labyrinths with the level sequence 3 2 1 4 7 6 5 are shown. The first image shows the alternating Cretan type, the second and third images show non-alternating labyrinths with the same level sequence. In the second image, the pathway traverses the axis when changing from the 1st to the 4th circuit. In the third image it traverses the axis from the 4th to the 7th circuit. (There is an other labyrinth with the pathway traversing the axis twice, first from the 1st to the 4th and second from the 4th to the 7th circuit). We thus are here presented with the only one alternating and several non-alternating types of labyrinths with the same level sequence.

Now there is a simple solution, to take account of this in the level sequence. For this it has to be considered, that the single numbers (not numerals) of the level sequence are separated. This separation can be obtained in different ways, using blanks, commas, semicolons etc. These separators, however, can also be used to indicate how the path will continue on the next level. Therefore we could e.g. define: if the path changes direction from the former to the next circuit, we will separate the numbers with a vertical slash. If, on the other hand, the path continues in the same direction and thus traverses the axis, we separate with a hyphen. This enables us to specify the level sequence so that it is unique also in non-alternating labyrinths. I show this in figure 2 using the images from figure 1.

uf_3214765_mit_tz

Figure 2. Level Sequence with Separators


Here we see for each labyrinth the unique level sequence with separators. The sequence of numbers is the same 3 2 1 4 7 6 5 in all three labyrinths. However, whereas in the alternating Cretan type all numbers are separated by slashes (as the path always changes direction when progressing from one circuit to an other), the level sequence in the second labyrinth is written with a hyphen between 1 and 4, and the level sequence in the third image with a hyphen between 4 and 7.

Indeed, the notation can be even simplified by separating with blanks and using hyphens only to indicate where the pathway traverses the axis. The level sequences would then be written as follows:

for the  1st image: 3 2 1 4 7 6 5
for the  2nd. image: 3 2 1-4 7 6 5
for the  3rd image: 3 2 1 4-7 6 5

What matters is that in the level sequence it is indicated where the path traverses the axis. With this specification it is now possible to give a unique level sequence to each course of the pathway and thus a unique name to each alternating and non-alternating type of labyrinth.

Related posts

Read Full Post »

And vice versa: How to make a Wunderkreis from a Babylonian visceral labyrinth.

That’s possible, at least with the Babylonian Umma Labyrinth.

The essentials of a labyrinth ly in the course of the pathway expressed by the level sequence, not the external form or layout. More exactly Andreas calls this the pattern.

The Babylonian Umma Labyrinth

The Babylonian Umma Labyrinth

The Umma labyrinth has two turning points surrounded by two circuits each and a meander in the middle. The two entries ly outside. There is only one, unequivocal way through the labyrinth.

The Wunderkreis has a double spiral in the centre and two other turning points with arbitrarily many circuits. Besides, a side has a circuit more than the other. The entries are in the middle section.

A large Wunderkreis

A large Wunderkreis

In order to indicate the single developing steps I first transform a “completely developed” Wunderkreis into the smallest possible version.

It looks thus: A meander in the middle and two other turning points with a total of three circuits as to be seen in the labyrinth type Knossos.

The smallest Wunderkreis

The smallest Wunderkreis

To be able to compare this small Wunderkreis to the Umma labyrinth, I lay all centres (at the same time the ends of the boundary lines or the turning points) on a single line. Just as if I folded the triangle built from the turning points.

The compressed Wunderkreis

The compressed Wunderkreis

Both entries are here in the middle section, in the Umma labyrinth they are outside and side by side. Besides, there is one more circuit on the left side. Now I add one circuit to the figure and the entry will change to the outer side on the right as well.

One more circuit

One more circuit

I now turn the second entry to the left side. As a result, the two entries  point in different directions.

The two entries outside

The two entries outside

Hence, I turn the right entry completely to the outer side on the left beside the left entry. As I do that geometrically correct, two empty areas appear.

The two entries side by side

The two entries side by side

Now I extend both entry paths by a quarter rotation upwards and turn the whole figure to the right by some degrees . Thus I receive the complete Umma labyrinth.

The Babylonian Umma Labyrinth

The Babylonian Umma Labyrinth

If I want to develop the Wunderkreis from the Umma labyrinth, I must leave out some circuits, turn the whole figure and finally raise the middle part.

The nucleus

The nucleus

The supplements made in the preceding steps are emphasised in colour. The nucleus of the visceral labyrinth contains the Wunderkreis.

Surely the Wunderkreis as we know it nowadays was not developed in this way. There are no historical documents to prove that. However, in my opinion the relationship of both labyrinth figures can be proved thereby. They are not simply spirals or meanders. These elements are rather included and connected in a “labyrinthine” way.

Related Post

Read Full Post »

Type or Style / 6

What is a Type

What is interesting in labyrinths is the manner in which the pathway takes it’s course through the labyrinth. Therefore I use exclusively the course of the pathway for a typology. This is the approach that is already recognizable in Kern, although it has not been elaborated to a full typology yet.

The course of the pathway can be represented in different ways, for instance by using the level sequence or with the pattern. To me the pattern is the easier way. Therefore my rule is: labyrinths with the same pattern are of the same type. Labyrinths with different patterns belong to different types.

RF Kretisches Labyrinth

 

 

 

 

 

All labyrinths with this pattern are of the Cretan Type

RF Reims

 

 

 

 

 

 

All labyrinths with this pattern are of the Reims Type

RF Chartres

 

 

 

 

 

 

All labyrinths with this pattern are of the Chartres Type

asf.

I have already described here at length how the pattern can be obtained (see realted posts below).

Erwin sometimes uses the level sequence to describa a type of labyrinth. This has the great advantage, that a type is directly given a name (even though a somewhat abstract one). So, for instance, type 3 2 1 4 7 6 5. However, there are two reasons, why I do not use the level sequence:

  • Only in alternating one-arm labyrinths, there exists exactly one type of labyrinth for each level sequence. If we also consider non-alternating labyrinths where the pathway traverses the axis, there can exist multiple types of labyrinths for the same level sequence.
  • In many labyrinths with multiple arms the level sequence is much longer and more complex and therefore less understandable.

This is why I use the pattern for the classification of labyrinths. This approach has advantages and disadvantages.

Advantages
Types of labyrinths can be clearly defined. Each labyrinth example can be unequivocally assigned to a type. The typology is given in the form of a rule. One has to know and apply this rule. Therefore it is not necessary to provide all possible types in advance. It is sufficient to keep a listing of the types that have already been realized. If a new type is discovered or designed, this can be easily added to the existing ones.

Disadvantages
A countless number of types are thinkable. However, in practice, it can hardly be expected that ten thousands or even thousands of types of labyrinths will persist. Rather I expect it to be some hundreds. There exist about 100 different historical types of labyrinths. A comprehensive list of all contemporary labyrinths is missing. Also, many designs and sketches may fall into oblivion. However, theoretically there is a vast number of possible types of labyrinths. This can be already seen from Tony Phillips’ work, that is limited to alternating one-arm labyrinths.

It is therefore necessary to aggregate the types of labyrinths on higher levels. For instance they could be aggregated to sub-groups, groups and families or else. This, however, is also a necessity in other typologies. We have seen this already in the typologies by TLS and BL.

Related Posts:

Read Full Post »

About the Order of Labyrinths

Sometimes it may occur that your attention is attracted by a new labyrinth, or that you create a labyrinth yourself. Of course in such cases one would like to know, whether such a labyrinth already exists, or if it is something original? To answer this question, a typology of labyrinths is needed. It would then be possible to compare the labyrinth in question with the typology. Therefore a typology should

  • group similar labyrinths into types
  • allocate different labyrinths to different types
  • make transparent how the types were defined
  • allocate the individual examples unambigously i.e. using consistently the same criteria
  • cover the range of the known labyrinths
  • be open so that up to now unknown labyrinth types can be added.

How then should the individual labyrinths be ordered, classified?

Typ:Stil

How to Classify?

There are various approaches to order the multitude of labyrinths. First of all, of course, the work of Hermann Kern, Through the Labyrinth°, has to be mentioned. Kern had collected and ordered the full available material about labyrinths and mazes. His objective, however, was not to elaborate a typology of labyrinths. He wanted to document the first rise and appearance of the labyrinth-figure and to reconstruct its further proliferations. Kern ordered the labyrinths primarily in chronological order. In the course of the historical development, he found various typical forms. Kern explicitly applied some types of labyrinths, particularly the Cretan type and the Chartres type.

The order of labyrinths by Kern has influenced many following attempts. For instance the compilation of 100 labyrinths in a chronological / geographical order by Eichfelder. Or, similarly, the overviews by Edkins or Jensen. These compilations, however, have not been conceived as typologies.

The Labyrinth Society, on its website, presents a dedicated typology. This typology, in part follows the order of labyrinths by Kern, but also substantially deviates from it. However, this typology is incomplete and in-transparent. The occupation with this typology has made me identify the classical style.

A comprehensive typology can be found on the website Begehbare Labyrinthe. This typology applies to the labyrinths compiled in the catalogue of walkable labyrinths of this website and in this respect is complete. Several original types of labyrinths can be found in this typology, however, this is not often made clear.

Erwin has repeatedly stated on this blog, that for him the sequence of the path is the criterion that determines the types of labyrinths. However, he does not apply this rule consistently.

For the distinction of types of labyrinths I exclusively use one criterion: the pattern. Thus it is also immediately clear how the individual examples are allocated to a particular type of labyrinth. Erwin and myself agree with each other to a great extent.

A great issue in the typology of labyrinths is that “type” and “style” are often confused. This said, I have to add that I am rather hazy about what I here just refer to as “style”. This still has to be elaborated more clearly. Therefore, in following posts I will try to distinguish between type and style and to clarify their relationship.

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

Read Full Post »

Inverting a labyrinth brings us to the dual labyrinth of it. If we now invert the Cretan-type labyrinth, we will obtain another Cretan-type labyrinth, although with the entrance on top.

O-D Kretisch

Figure 1. Inverting the Cretan-type Labyrinth

Fig. 1 shows the process and result of this inversion.

In order to compare the original and dual labyrinths, as previously shown, we isolate the dual labyrinth and carry-over the pattern on it. Then we rotate the dual labyrinth with the pattern lying on it, so that it is directed with the entrance from below, and place it next to the original labyrinth.

SD Kret

Figure 2. The Original and Dual Labyrinths are the Same: Self-dual

As shown in Fig. 2, the original and dual labyrinths are the same. The two labyrinths that are dual to each other have the same pattern, although the pattern is rotated by 180°. This is the case here too. So the right image really shows the pattern rotated by 180°. However, this pattern, after it has been rotated, is self-covering. This is not the case in “normal” dual labyrinths.

Now let us also have a look at the level sequences. As the Cretan-type labyrinth has 7 circuits, we need to use 7 colors.

UF 7 Farben

Figure 3. The Colors of the Circuits

Fig. 3 shows the sequence of the colors. In addition to the first five colors from our last post, we use the color Bordeaux for the circuit that is covered as the 6th and orange for the circuit that is covered as the last by the pathway.

UF Muster Kret

Figure 4. Level Sequences in the Pattern

Fig. 4 shows the level sequence directly on the pattern. As usual, the left image indicates the level sequence into the original and out of the dual labyrinth, whereas the right image indicates the level sequence into the dual and out of the original labyrinth. Both level sequences are identical.

Labyrinths in which the original and dual labyrinths are the same, are referred to as self-dual. These are particular labyrinths and they have a higher inner order than “normal” dual labyrinths.

Muster d sd

Figure 5. Pattern of a Dual (left) and Self-dual (right) Labyrinth

This can also be seen in comparing the patterns of dual and self-dual labyrinths (fig. 5). In dual labyrinths (left image), the courses of the first (grey) and the second (black) halves of the pathways are different, whereas they are congruent in self-dual labyrinths (right image).

Some of the most excellent labyrinths are self-dual, such as the Otfrid, Chartres, Reims, Auxerre, Saffron Walden and some others.

Related posts:

Read Full Post »

Older Posts »

%d bloggers like this: