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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.

And here is a template to make such a cube:

Template

Template

If you want, you can download, print, copy or view this 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 Link

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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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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

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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

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Sector Labyrinths

At the end I will also transform a sector labyrinth into the MiM-style. What is special in sector labyrinths is, that the pathway always completes a sector first, before it changes to the next. As a consequence of this, the pathway only traverses each side-arm once. Thus it seems, that sector labyrinths may be easier transformed into the MiM-style than other labyrinths with multiple arms. I will use as an example a smaller labyrinth with four arms and five circuits. There exist several labyrinth examples of this type. I have named it after the earliest known historical example, the polychrome mosaic labyrinth that is part of a larger mosaic from Avenches, canton Vaud in Switzerland.

Figure 1. Sector Labyrinth (Mosaic) of Avenches

Figure 1 shows the original of this labyrinth (source: Kern 2000: fig 120, p 88). It is one of the rarer labyrinths that rotate anti-clockwise. On each side of the side-arms it has two nested turns of the pathway and 3 nested turns on each side of the main axis. The pattern corresponds with four double-spiral-like meanders arranged one after another – Erwin’s type 6 meanders (see related posts 2). When traversing from one to the next sector the pathway comes on the outermost circuit to a side-arm, traverses this on full length from outside to inside and continues on the innermost circuit in the next sector.

In order to bring this labyrinth into the MiM-style, first the origninal was mentally rotated so that the entrance is at bottom and horizontally mirrored. By this it presents itself in the basic form, I always use for reasons of comparability. Fig. 2 shows the MiM-auxiliary figure.

Figure 2. Auxiliary Figure

This has 42 spokes and 11 rings what makes it significantly smaller than the ones for the Chartres, Reims, or Auxerre type labyrinths. The number of spokes is determined by the 12 ends of the seed pattern of the main axis and the 10 ends of each seed pattern of a side-arm.

In fig. 3 the auxiliary figure together with the complete seed pattern including the pieces of the path that traverse the axes is shown and the number of rings needed is explained. For this the same color code as in the previous post (related posts 1) was used.

Figure 3. Auxiliary Figure, Seed Pattern and Number of Rings

As here the angles between the spokes are sufficiently wide, it is possible to use all rings of the auxiliary figure for the design of the labyrinth. We thus need no (green) ring to enlarge the center. Only one (red) ring is needed for the pieces of the path that traverse the axes – more precisely: for the inner wall delimiting them –, four (blue) rings are needed for the three nested turns of the seed pattern of the main axis, one ring (grey) for the center, and five rings (white) for the circuits, adding up to a total of 11 rings.

Fig. 4 finally shows the labyrinth of the Avenches type in the MiM-style.

Figure 4. Labyrinth of the Avenches Type in the MiM-Style

The figure is significantly smaller and easier understandable than the labyrinths with multiple arms previously shown in the MiM-style. Overall it seems well balanced, but also contains a stronger moment of a clockwise rotation that is generated by the three asymmetric pieces of the pathway and of the inner walls delimiting these on the innermost auxiliary circle.

Related posts

  1. How to Draw a MiM-Labyrinth / 14
  2. How to Find the True Meander for a Labyrinth

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For Year 2019 we wish you all the best and interesting encounters with the labyrinth.

Labyrinth with 7 Axes, 15 Circuits and 6 Nested Turns at Both Sides of Each Axis, and yet no Sector Labyrinth – Rather the Opposite, Self-dual

 

 

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Wishing all visitors of this Blog a Merry Christmas and a Happy New Year!

An 11 circuit Christmas tree labyrinth

An 11 circuit Christmas tree labyrinth

Related Posts

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