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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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For a better view

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My co-author Andreas Frei reported in his last article about the labyrinth drawing rejected by Sigmund Gossembrot on folio 53 v. And thereby made the amazing discovery that in it principles of design have been applied to which so far not one known historical labyrinth was developed.
Not for the sector labyrinths of the Roman labyrinths or the various Medieval ones. Even among the contemporary labyrinths (for example, the London Underground’s 266 new types by Mark Wallinger), this new type does not show up.

However, the labyrinth derived by Andreas Frei has some extraordinary features that I would like to describe here in more detail.
First of all see a representation of the new type in concentric style:

The 7 circuit labyrinth of folio 53 v in concentric style

The 7 circuit labyrinth of folio 53 v in concentric style

Contained is the classic 7 circuit labyrinth, as it can be developed from the basic pattern. In the upper area and in the two side parts 3 barriers are inserted, which run over 4 courses and again create 6 new turning points. These barriers are arranged very evenly, they form an isosceles cross. This significantly changes the layout.

The entrance to the labyrinth is on lane 3, then in the 1st quadrant on the lower left side you immediately go to the lanes 6, 5, 4 and 7. Thereby the center is completely encircled (in all 4 quadrants).
In the 4th quadrant on the bottom right, you go back over the lanes 6, 3, 2 through the remaining quadrants to the 1st quadrant.
From here, you go around the whole labyrinth, in the 4th quadrant, you quickly reach the center via the lanes 4 and 5.
Twice the entrance is touched very closely: at the transition from lane 2 to 1 in the 1st quadrant and at the transition from lane 1 to 4 in the 4th quadrant.

Fascinating are also the two whole “orbits” in lanes 7 and 1. The two semicircles in lane 2 are remarkable too. Lanes 3, 4 and 5 are only circled in quarter circles.

All this results in a unique rhythm in the route, which appears very dynamic and yet balanced.

Of course, this is hard to understand on screen or in the drawing alone. Therefore, it would be very desirable to be able to walk such a labyrinth in real life.

So far there is no such labyrinth. Who makes the beginning?

The centered labyrinth of folio 53 v

The centered labyrinth of folio 53 v

This type can also be centered very well. This means that the input axis and the entrance axis can be centrally placed on a common central axis. This results in a small open area, which is also referred to as the heart space.

Also in Knidos style, this type can be implemented nicely. This makes it even more compact. However, the input axis is slightly shifted to the left, as it is also the case in the original.
Here the way, Ariadne’s thread has the same width everywhere.

The labyrinth of folio 53 v in Knidos style

The labyrinth of folio 53 v in Knidos style

And here, as a suggestion to build such a labyrinth, the design drawing for a prototype with 1 m axle jumps. The smallest radius is 0.5 m, the next one is 1 m larger.
With a total of 11 centers, the different sectors with different radii can be constructed.

The design drawing

The design drawing

The total diameter is depending on the width of the path at about 18 m, the path length would be 225 m.

As the axes of the path are dimensioned, Ariadne’s thread is constructed.
All dimensions are scalable. This means that the labyrinth easily can be enlarged or reduced.

And here you may download or print the drawing as a PDF file.

Related Posts

Sigmund Gossembrot / 3

The Labyrinth on Folio 53 v

Originally I had intended to show the design on folio 53 v already in my previous post (see related posts, below). It can be seen as a mistaken attempt to the labyrinth on fol. 51 r. But then I took a closer look at it. And the result has prompted me to dedicate a separate post to this design. Fig. 1 shows the design on fol. 53 v.

Figure 1. Labyrinth on folio 53 v

The design on fol. 53 v was rejected, crossed out and overwritten with text. It is clearly recognizable a five-arm labyrinth with 7 circuits. Also the design of the side-arms is very similar as in the labyrinth on fol. 51 r.
As the labyrinth on fol. 51 r, also this labyrinth rotates anti-clockwise. In fig. 2 I have mirrored it, inscribed the Ariadne’s Thread and in parallel presented the pattern. The Ariadne’s Thread traverses the lines of the labyrinth in two places. These are marked with blue circles. I have assumed that these were still provisional auxiliary lines that would have been removed if the final version of this labyrinth had been completed.

Figure 2. Ariadne’s Thread and Pattern

The result is surprising. Segment 4 is not filled out by the pathway. The path on the innermost and the two outer circuits passes this segment and marks only the left side of the third and the right side of the fourth side-arm. In addition the main axis includes one superfluous axial piece of the path. The pathway leads into the center, and a second piece of the path in the center of the main axis leads from the center into a dead-end.

This design can be easily corrected such that there results a four-arm unicursal labyrinth as shown in fig. 3.

Figure 3. Corrections

In order to achieve this, each of the two pairs of walls delimiting the pathway drawn in blue must be shifted against another until they come to lie one above the other. This results in the extinction of the fourth segment and of the central piece of the pathway with the dead-end on the main axis.

Figure 4 shows the new pattern and the four-arm labyrinth derived from it.

Figure 4. The Labyrinth Hidden in the Draft on Fol. 53 v

So, in the rejected five-arm design, a four-arm labyrinth is contained or hidden. The course of the pathway of this follows about the same principle as in the labyrinth on fol. 51 r. I am not aware of any existing labyrinth of this type.

Related Posts:

In the context of the theme Labyrinth and Flower of Life, the similarity to a cube has been mentioned more often. The hexagonal shape of the labyrinth was just too reminiscent of a cube. And that got me looking for the labyrinth on the cube.

I have a magic cube and as a small brain training I solve it once a day. This is now memorized and routinely.

In Further Link below you can find out what a magic cube is.

First, I tried to put Ariadne’s thread on the small squares. This is relatively easy.

For better representation, the 6 sides of a cube are “flattened”:

The layout

The layout

You can draw in there Ariadne’s thread for a 3 circuit labyrinth type Knossos. Generally known, this has the path sequence: 3-2-1-4.
The beginning is on the frontside below at left. Then we go to the third line, to the second and the first line and finally to the center in 4 up in the middle square.

Ariadne's thread

Ariadne’s thread

And here in an isometric view:

Three views

Three views

I hope you can imagine that on the drawings?
We see the lines on 5 sides of the cube, the bottom remains empty. The middle is slightly larger, but we do not touch all the small squares.

Ariadne’s thread for the template with slightly thicker lines:

Ariadne's thread

Ariadne’s thread

If you want, you can download, print or copy the template as a PDF file.

Such a cube would certainly be quite easy to solve as a magic cube. Especially if you have a template of it in mind.

Related Posts

Further Links

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

Almost seven years ago, the flower of life was a topic in this blog. Now I would like to add a few things.
First, the original drawing of Ariadne’s thread in the flower of life. During a visit to Salzburg, Marianne Ewaldt asked me if the labyrinth was included in the flower of life. She gave me a small anniversary publication for the 80th birthday of Dr. Siegfried Hermerding, which was titled “The Flower of Life and the Universe”. It contained countless symbols and prototypes, but not a labyrinth.

Ariadne's Thread in the Flower of Life

Ariadne’s Thread in the Flower of Life

This is the picture to which I drew Ariadne’s thread for the three-circuit labyrinth on 25 June 2012 in Salzburg.

What is it about the flower of life? A sober and rational answer comes from Wikipedia :

An overlapping circles grid is a geometric pattern of repeating, overlapping circles of equal radii in two-dimensional space. Commonly, designs are based on circles centered on triangles (with the simple, two circle form named vesica piscis) or on the square lattice pattern of points.

Patterns of seven overlapping circles appear in historical artefacts from the 7th century BC onwards; they become a frequently used ornament in the Roman Empire period, and survive into medieval artistic traditions both in Islamic art (girih decorations) and in Gothic art. The name “Flower of Life” is given to the overlapping circles pattern in New Age publications.

Many see much more in the flower of life. They may, but one should not overemphasize. From the labyrinthine point of view, it remains to be noted that it is a grid in which, depending on the size, different labyrinths can be accommodated. They always have a hexagonal shape and a cube-shaped appearance. It’s a style similar to the labyrinths in man-in-the-maze style, as Andreas has explained in several articles.

In the articles mentioned below further drawings and derivations of Andreas and me can be found.

To accommodate a 7-circuit labyrinth in the Flower of Life, you have to extend the grid of full circles, as Andreas has stated. Marianne Ewaldt did that as a ceramic artist and gave me as present such a labyrinth last year.

A Golden Ariadne's Thread in th Flower of Life

A Golden Ariadne’s Thread in th Flower of Life

And here is another drawing of me with all the lines of the labyrinth in a slightly larger grid:

The complete 7-circuit classical labyrinth

The complete 7-circuit classical labyrinth

It can be clearly seen that the outer boundary lines form a hexagon and also depict a cube.

Related Posts

Further Link

Labyrinth Designs – Overview

Sigmund Gossembrot the Elder, humanist and mayor of Augsburg, had compiled a miscellany around 1480 (siehe below: literature 1). Into a text in Latin on the seven arts were included nine labyrinth drawings, all executed in brown ink on paper (Kern, p. 139 / 140, see literature 2). This manuscript is accessible online in an unprecedented quality (see below: further links 1) and is licensed under a Creative Commons Attribution – NonCommercial – ShareAlike 4.0 International License (see below: further links 2).

The following figures have been obtained by copying and cropping the image files of the Münchener DigitalisierungsZentrum, Digitale Bibliothek. They can be found on sheets, folios (fol.) 51-54, each on the front-side r (= recto) and back side v (= verso). Here I first want to present a global overview. The links on the captions’ references to the folios directly lead to the corresponding pages of the online edition of the manuscript. Here you will be linked directly to a preview with miniatures of the pages. From there you can zoom in the pages or browse the manuscript. I strongly recommend to take a look at the manuscript, that is worth it!

Fig. 1 shows a five-arm labyrinth with seven circuits and a central pentagram.

Figure 1. Labyrinth on Fol. 51 r

 

Fig. 2 shows a circular, four-arm labyrinth with eight circuits.

Figure 2. Labyrinth on Fol. 51 v

In fig. 3 another circular, four-arm labyrinth with eight circuits and a somewhat differing course of the pathway is depicted.

Figure 3. Labyrinth on Fol. 52 r

Fig. 4 shows the upper, fig. 5 the lower of two square form labyrinths each with four arms and eight circuits. The uppper has the same course of the pathway as the labyrinth in fig. 3, the lower the same as the one in fig. 2.

Figure 4. Labyrinth on Fol. 52 v oben

 

Figure 5. Labyrinth on Fol. 52 v unten

In fig. 6 we see a circular one-arm labyrinth with nine circuits.

Figure 6. Labyrinth on Fol. 53 r

Fig. 7 shows an incomplete labyrinth that was crossed out with recognizably five arms and seven circuits.

Figure 7. Labyrinth on Fol. 53 v

In fig. 8 a complex labyrinth with 12 circuits can be found.

Figure 8. Labyrinth on Fol. 54 r

Finally, fig. 9 shows a circular one-arm labyrinth with 11 circuits.

Figure 9. Labyrinth on Fol. 54 v

Some of these labyrinth designs include types of labyrinths of their own, others are of existing types, some of which with unchanged course of the path, whereas in others the course of the path was modified to a multicursal maze. I will come back to this more in detail in the next posts.

Literature

  1. Gossembrot, Sigismundus: Sigismundi Gossembrot Augustani liber adversariorum, 15. Jh. München, Bayerische Staatsbibliothek, Clm 3941.
  2. Kern, Hermann: Through the Labyrinth: Designs and Meanings over 5000 years. London: Prestel 2000.

Further Links

  1. Gossembrot, Sigismundus: Sigismundi Gossembrot Augustani liber adversariorum
  2. Terms of Use

World Labyrinth Day 2019

Again you are invited from The Labyrinth Society to celebrate the World Labyrinth Day:

Celebrate the 11th Annual World Labyrinth Day on May 4, 2019 and join over 5,000 people taking steps for peace, ‘Walking as One at 1’ in the afternoon. Last year there were participants in over 35 countries.

Flyer TLS

A small, but global Wunderkreis on the flyer of the TLS

Most nicely it would be if everybody which is able would walk a labyrinth. But it is also possible, as a substitute to trace a finger labyrinth, to make a labyrinth meditation or to be active labyrinthine in some way.

More here:

If you are looking for a labyrinth near you, maybe you will find one here:

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