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On my own behalf

Welcome to the Labyrinth

The topic of this blog is the labyrinth. Under nearly all aspects, I would like to arouse your interest on the fascinating lines and the meaning of this old object. Being an old surveyor I put my focus on the geometrical shape.
A new post should be published about twice a month. Meanwhile I am accompanied by Andreas Frei as coauthor.

Contents

In a blog the single posts (articles) are disposed in reverse order: the latest posts first, the older ones following. The display of the content is thus different from a website where it is always permanent.

Anyone who is looking for something special about labyrinths or just wants to know what can be found on this blog, maybe would like to have an overview.

I can provide this now and offer it as an own page titled Contents.

The register with the table of Contents is on top of the blog above the header image next to About us.

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It seemed obvious to apply the principles for two-parted 5 circuit labyrinths in the previous posts also for 7 circuit labyrinths.

For this purpose, the double barrier is extended to 6 passages, thus creating a triple barrier.

This is what it looks like:

A two-parted 7 circuit concentric labyrinth (entrance 3rd track)

A two-parted 7 circuit concentric labyrinth (entrance 3rd track)

It is noteworthy that both the entry into the labyrinth as well as the entry into the center is possible in and from the same circuit, here from the third circuit.
The path sequence is: 3-6-5-4-7-2-1-2-7-4-5-6-3-8

But it is also possible to design that from the 5th circuit. This creates a new type again.
Here is the example:

A two-parted 7 circuit concentric labyrinth (entrance 5th track)

A two-parted 7 circuit concentric labyrinth (entrance 5th track)

The path sequence is then: 5-4-3-6-7-2-1-2-7-6-3-4-5-8


And here are the two variants in Knidos style:

A two-parted 7 circuit labyrinth in Knidos style (entrance 3rd track)

A two-parted 7 circuit labyrinth in Knidos style (entrance 3rd track)

 

And here from the 5th circuit:

A two-parted 7 circuit labyrinth in Knidos style (entrance 5th track)

A two-parted 7 circuit labyrinth in Knidos style (entrance 5th track)

Now you could move the barrier and its related elements upwards. Then it would not be the first circuit who is completely gone through, but the innermost, the 7th circuit.

So the whole structure (pattern), expressed in the path sequence, would be changed. That would also create a new type of labyrinth again.

Here in a simplified representation:

A two-parted concentric 7 circuit labyrinth (entrance 3rd track)

A two-parted concentric 7 circuit labyrinth (entrance 3rd track)

Here with entrance in the 5th circuit:

A two-parted concentric 7 circuit labyrinth (entrance 5th track)

A two-parted concentric 7 circuit labyrinth (entrance 5th track)

But someone else had this idea. On the Harmony Labyrinths website, Yvonne R. Jacobs has introduced hundreds of new labyrinth designs and copyrighted them.

She calls these types Luna V (Desert Moon Labyrinth) and Luna VI (Summer Moon Labyrinth). On her website you can look at the corresponding drawings and even order finger labyrinths (only in the USA).

Related Posts

Further Link

Sigmund Gossembrot / 7

Summary

At the end I want to summarize some findings of the previous six posts on Gossembrot. In my opinion, two main aspects seem important.

New types of labyrinths

Gossembrot has created two labyrinths with unique courses of the pathway, and thus designed two new types of labyrinths. The five-arm labyrinth on fol. 51 r is an outstanding type of labyrinth. The one-arm labyrinth with nine circuits on fol. 53 r is one of the rarer non-alternating types of labyrinths. Furthermore, a third new type of a four-arm labyrinth is hidden in the drawing on fol. 53 v.

Gossembrot could also have been first in drawing the Schedel type labyrinth (fol. 51 v) or the scaled-up basic type (fol. 54 v). It is true, that the manuscript containing the Schedel type is dated somewhat earlier than the one by Gossembrot. However, the drawing in Schedel manuscript could also have been added later. The two earliest examples of the scaled-up basic type are dated from the 15 th century without further precision. Thus, they could also have been generated later than 1480. However, I think this is unlikely. Both examples (Hesselager and Sibbo) were desinged in the classical style – which is the style that best matches with the natural way of designing this type of labyrinth.

Approaches to mazes

Gossembrot was strongly involved with the difference between labyrinth and maze. This is well attested by the mazes he had derived from the labyrinths of the Schedel type (fol. 52 r and fol. 52 above) and, following an other approach, from the Chartres type (fol. 54 r). And also by the fact that Gossembrot took this complex labyrinth for his best labyrinth.

I think also that his rejected design on fol. 53 v is not a mistaken attempt to the five-arm labyrinth on fol. 51 r. But instead, it seems to me that this is a failed attempt to derive a maze from the five-arm labyrinth. This is particularly supported by the design of the main axis. This was amended in a similar way as the ones of the mazes (fol. 52 r and fol. 52 v above) Gossembrot had derived from the Schedel type labyrinth.

It was not until the 15 th century that the creation of mazes began. The first drawing of a maze by Giovanni Fontana dates from year 1420 (see literature below: p. 138, fig. 239). Gossembrot was one of the first to draw mazes. His mazes, however, are, even compared with some other ones by Fontana (literature, p. 238, fig. 240), still rudementary and are fully based on unicursal labyrinths.

Conclusion

Gossembrot undoubtedly has his great importance in the design of unicursal labyrinths. Even if he must have been very fascinated by the maze, such that he himself took a maze for his best labyrinth, his drawings still represent tentative approaches and attempts to mazes. Contrastingly, he has created awesome original designs with fundamental innovations in unicursal labyrinths.

Literature
Kern H. Through the Labyrinth – Designs and Meanings over 5,000 Years. Munich, London, New York: Prestel 2000.

Related Posts:

In dealing with the double-barrier technique in recent posts, I found this installation of Mark Wallinger’s Labyrinths on the London Underground:

The labyrinth 233/270 at the station Hyde Park Corner, Photo: credit © Jack Gordon

The labyrinth 233/270 at the station Hyde Park Corner, Photo: credit © Jack Gordon

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

The special feature of this is that two double barriers are located next to each other in the upper part of the central axis. In the routing chosen by him you move at the transition from the 2nd to the 3rd quadrant first away from the center.

I’ve changed that so much that you would “experience” a movement to the center in a walkable labyrinth.

This is what it looks like:

A new labyrinth in concentric style

A new labyrinth in concentric style

I have also moved the side double barriers and this makes the routing in all quadrants also different. So a new type of labyrinth is born.

Here in Knidos style:

A new centered sector labyrinth in Knidos style

A new centered sector labyrinth in Knidos style

Why not as a two-parted labyrinth?

A new two-parted 5 circuit labyrinth

A new two-parted 5 circuit labyrinth

The left part has the path sequence: 3-4-5-2-1 and the right part: 5-4-1-2-3, so there are two 5 circuit labyrinths in it.

And here again in Knidos style:

A new two-parted and centered 5 circuit labyrinth in Knidos style

A new two-parted and centered 5 circuit labyrinth in Knidos style

The remarkable thing about this type is that both the entry into the labyrinth in the 3rd lane takes place, as well as the entry into the center.

Related Posts

Sigmund Gossembrot / 6

The Complex Labyrinth

On folio 54 r, finally, is depicted the complex labyrinth shown in figure 1 (see also: related posts, below). In it’s center is written: „laborintus melior inter priores aquia magis errabunda inducens et educens“ – this labyrinth is better than the previous ones, as it is more misleading, leading in and out. This labyrinth has 12 circuits and its’ turns of the pathway are arranged in a confusing order. The number of arms cannot be easily counted.

Figure 1. The Complex Labyrinth on Folio 54 r

The pathway enters the labyrinth from below on the first (outermost) circuit (fig. 2). There it first bifurcates, and one can follow it in both rotational directions (clockwise or anticlockwise). On top of this circuit deviates another piece of the pathway. This then leads further into the labyrinth. Thus, the outermost circuit is designed not unicursally but multicursally as a maze.

Figure 2. The Outermost Circuit

The outermost circuit can be removed (fig. 3). This brings us to an autonomous core-labyrinth with 11 circuits. Additional circuits, however, cannot be simply removed without destroying the core-labyrinth. The core-labyrinth has clearly recognizable a main axis that is oriented to the top and it rotates clockwise.

Figure 3. Core Labyrinth

For a further investigation (in fig. 4) we now rotate the labyrinth, such that the main axis points to the bottom. By this, the labyrinth presents itself in the form we always use as a baseline. The main axis (in a blue frame) has exactly the same shape as the one of the Chartres type labyrinth. The other turns of the pathway are arbitrarily distributed over about the upper 2/3 of the area.

Figure 4. Main Axis

However, in view of the shape of the main axis the idea suggests itself, that also the remaining turns of the pathway could have something to do with the Chartres type. Indeed, three areas can be easily identified (fig. 5). The turns of the pathway inside these trapezoidal areas (red) can be aligned axially.

Figure 5. Side Arms

For this purpose, they need to be shifted along their circuits. Two turns of the path (the innermost of the 1st and 2nd side-arm are almost already in their right place. This is shown in fig. 6. The other ones need to be shifted further. This is illustrated with the red circles and arrows. In their new alignment they indeed result in a Chartres type labyrinth.

Figure 6. Type Chartres

Considered the other way round, we can state, that Gossembrot has derived a multicursal maze from the Chartres type labyrinth. For this, he has dispersed the regular order by shifting the turns of the pathway away from the side-arms and arbitrarily distributing them over the area of the labyrinth. Then he has attached a further circuit at the outside and on this circuit has introduced a multicursal course of the pathway.

Related Posts 

There are eight possibilities for a one arm 5 circuit labyrinth (see Related Posts below).

The structure of the different labyrinths can be expressed through the path sequence. Here is a list:

  1.  3-2-1-4-5
  2.  5-4-1-2-3
  3.  5-2-3-4-1
  4.  1-4-3-2-5
  5.  3-4-5-2-1
  6.  1-2-5-4-3
  7.  1-2-3-4-5
  8.  5-4-3-2-1

The sector labyrinth presented in my last post (see Related Posts below) has a different path sequence in all 4 quadrants. In other words, there are 4 different labyrinths hidden in it. These were the path sequences in the 1st to the 4th line of the list above.


Today another 5 circuit sector labyrinth modeled with Gossembrot’s double barrier technique:

A new 5 circuit sector labyrinth in concentric style

A new 5 circuit sector labyrinth in concentric style

The path sequence in quadrant I is: 3-4-5-2-1, in quadrant IV: 1-2-5-4-3. These are the aforementioned courses at the 5th and 6th place. The two upper quadrants have: 1-4-3-2-5 and 5-2-3-4-1. These correspond to the upper pathways at the 4th and 3rd places. Not surprising, because the transition in these sector labyrinths takes place either on the 1st or the 5th course.

Here in a representation that we know from the Roman labyrinths:

The new sector labyrinth in square shape

The new sector labyrinth in square shape

Or here in Knidos style:

The new sector labyrinth in Knidos style

The new sector labyrinth in Knidos style

On Wikimedia Commons I found this picture of Mark Wallinger’s unique Labyrinth installation at Northwood Hills station, installed as part of a network-wide art project marking 150 years of the London Underground. It is part of the emboss family (one of the 11 labyrinth design families).

Mark Wallinger Labyrinth 10/270, Photo: credit © Jack Gordon

Mark Wallinger Labyrinth 10/270, Photo: credit © Jack Gordon

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.


Now only two path sequences are missing, then we would have the eight complete.
There is also a new sector labyrinth for this:

Another new sector labyrinth in concentric style

Another new sector labyrinth in concentric style

In the two lower quadrants we have the courses 1-2-3-4-5 and 5-4-3-2-1. These are the above mentioned pathway sequences at the the 7th and 8th places. The upper two sequences (5-2-3-4-1 and 1-4-3-2-5) are again identical to the aforementioned two labyrinths and the one in the previous post.

The quadratic representation shows that it is actually a mixture of serpentine type and meander type (see Related Posts below).

The new sector labyrinth in Roman Style

The new sector labyrinth in Roman Style

Here in Knidos style:

The new sector labyrinth in Knidos style

The new sector labyrinth in Knidos style

Simply put, in only three sector labyrinths can all theoretically possible eight 5 circuit labyrinths be proved.


But it is also possible to move the “upper” pathways down, so that again arise new display options.
Then you can swap the right and left “lower” quadrants.
Or mirror everything and create right-handed labyrinths.

Here are two examples:

Even one more new sector labyrinth in round shape

Even one more new sector labyrinth in round shape

Another new sector labyrinth in Knidos style

Another new sector labyrinth in Knidos style

Related Posts

Sigmund Gossembrot / 5

The Two One-arm Labyrinths

Among the nine drawings by Gossembrot are also two one-arm labyrinths (see related posts, below).

The labyrinth on fol. 53 r has 9 circuits (fig. 1). In the center is written: inducens et educens, leading in and leading out. The design of the axis with it’s rhombus shape is eye-catching.
This almost looks a bit like an anticipation of the Knidos style… Furthermore, this is a non-alternating labyrinth. The pathway traverses the axis when changing from the 6th to the 9th circuit. I have highlighted this position in the labyrinth with two dashed red lines. To these correspond the dashed lines in the pattern. This pattern appears for the first time in the labyrinth by Gossembrot. Therefore it is a type of it’s own. I refer to it as type Gossembrot 53 r.

Figure 1. The Labyrinth on Folio 53 r

The labyrinth on fol. 54 v has 11 circuits and is designed in the concentric style (fig. 2). This type of labyrinth is also referred to as the scaled-up basic type or scaled-up classical / Cretan type of labyrinth. This, because the seed pattern in the classical style consists of a central cross with two nested angles and a coaxial bullet point between each two arms of the cross. The seed pattern of the basic type is made-up of a central cross with one angle and bullet point between each two arms of the cross.

Figure 2. The Labyrinth on Folio 54 v

There exist several historical examples of this type of labyrinth. The two earliest examples (fig. 3) are frescos in the church of Hesselager, Fünen, Denmark and in the church of Sibbo, Finnland (see literature, below).

Figure 3. Earliest Historical Examples (15 th Century)

Both were dated from the 15 th century without any further precision. Also, Gossembrot 54 v dates from the 15 th century (1480). Therefore, based on the dating, it is not possible to certainly identify the earliest preserved example of this type of labyrinth. So it is even conceivable, that the drawing by Gossembrot is earliest and thus Gossembrot was also the originator of this type of labyrinth.

Literature
Kern H. Through the Labyrinth – Designs and Meanings over 5000 Years. München, London, New York: Prestel 2000. P. 280, fig. 593; p. 281, fig. 601.

Related Posts:

I was particularly fascinated by the technique of double barriers in Gossembrot’s 7 circuit labyrinths presented in recent posts. This makes possible completely new types of labyrinths. He probably did not “invent” the double barriers, but he was the first to consistently and systematically use them.

How does this technique affect 5 circuit labyrinths?
I tried that and came across a whole new kind of sector labyrinths.
As you know, one sector after another is traversed in these before the center is reached.

The historical Roman labyrinths are divided into three different variants: the meander type, the spiral type and the serpentine type (see the Related Posts below).
The entry into the labyrinth is usually up to the innermost lane. And in all four sectors the structures are the same.
The change to the next sector either always takes place outside or even once inside (or alternately).

Now the new type:

The new sector labyrinth in concentric style

The new sector labyrinth in concentric style

What is so special about that?
Already the entrance: It takes place on the 3rd lane. This does not occur in any historical sector labyrinth. And the entrance into the center is also from the 3rd lane.

Then the structure expressed by the path sequence is different in each quadrant.

Quadrant I:   3-2-1-4-5
Quadrant II:  5-2-3-4-1
Quadrant III: 1-4-3-2-5
Quadrant IV: 5-4-1-2-3

The transitions to the next sector are always alternately.

Nevertheless, the new labyrinth is very balanced and mirror-symmetrical.

Here in a square shape:

The new sector labyrinth in square shape

The new sector labyrinth in square shape

This makes it easier to compare with the previously known Roman labyrinths (see below), which are mostly square.

The difference to these becomes clear especially in the presentation as a diagram. Because this shows the inner structure, the pattern.

The diagram for the new sector labyrinth

The diagram for the new sector labyrinth

Very nice to see are the nested meanders.

But even in Knidos style, this type is doing well:

The new sector labyrinth in Knidos style

The new sector labyrinth in Knidos style

How should one call this type? And who builds one as a walkable labyrinth?

Related Posts

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