# How to Generate the Seven Times Seven Labyrinth

For New Year I have presented the Seven Times Seven labyrinth (see: related posts 1, below). Erwin has immediately commented and noticed the similarity with the type Gossembrot 51 r. This is correct. I wanted to develop a self-dual labyrinth based on this type. And I wanted to preserve the typical characteristics of the course of the pathway. Typical for Gossembrot’s labyrinth are not only the double-barriers, but also the manner in which the path is directed through all segments. It is not a sector labyrinth, but rather in about the opposite of that.

In figure 1, I show the pattern of the Gossembrot 51 r type labyrinth. This serves as the starting point (a) and is presented in grey. I have already described earlier, what characterizes the course of the pathway (related posts 2). This happens in segments III to V. Another speciality is the meander in segment II. This meander lies on the circuits 2 – 6. So there is one more circuit each outside and inside of the meander.
First, I isolate the segment that contains the meander (b). The meander itself is self-dual. And, since there are added one more circuit each, at the outside and inside, the whole figure (b) is self-dual too. To this figure are attached on the right side segments III – V. These contain the typical course of the pathway by Gossembrot. From the fact, that segment II is self-dual, it also follows that one of its sides can be connected with a figure that is the dual to the figure connected with its other side. In a second step, therefore, I pick out the figure in segments III – V and place it to the right side of segment II. Figure (c), thus, shows nothing else than segment II not connected with segments III – V of the pattern of Gossembrot 51 r.

Figure 1. Preparation

This figure (c) forms the basis for the generation of the Seven Times Seven labyrinth, or of it’s pattern respectively. The process is shown in fig. 2. Here we begin in the third row with the figures colored in grey (c). In a third step, the figure from segments III – V is now duplicated (d). This duplicate is then rotated by 180 degrees in a fourth step. This produces the dual figure of it (e). Then we shift it downwards and can see: it can be connected to the left side of the figure with the meander from segment II (f). Now we only have to really connect these elements with each other and by this obtain in figure (g) the pattern of the Seven Times Seven labyrinth.
This whole pattern is self-dual. The number of segments has increased from the five segments of the labyrinth type Gossembrot 51r to new seven segments. The dual of Gossembrot’s segments III – V covers the new segments I – III, the meander with its additional circuits inside and outside follows in central segment IV, and Gossembrot’s original segments III – V are here shifted to segments V – VII.

Figure 2. Generation of the Pattern

Figure 3 shows the labyrinth in the basic form without the heptagram in the center and without the heptagon at the periphery. These are add-ons and have to be attributed to the style, rather than to the type of labyrinth.

Figure 3. The Labyrinth in Base Form

A very well balanced labyrinth. The main axis looks the same as in the basic type. Opposite to the main axis, in the central segment IV, lies the meander. In three segments before and after the meander, the typical course of the pathway can be found. The path proceeds in wrapping or wrapped curve through all segments, thereby passing the meander and arrives in a backward movement through sectors VII – V in sector IV, through which it continues as meander, then continues its backward movement through sectors III – I, from where it leads in forward direction through all segments to the center.

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# The Dual Labyrinth Type Gossembrot 51 r

In one of his articles, Andreas introduced the relatives of the labyrinth type Gossembrot 51 r.

The labyrinth type Gossembrot 51 r centered and in concentric shape

Today I want to take a closer look at the dual version.
I particularly like this. This is because the outermost circuit (1) lead around all sectors. In the original, the innermost (7) completely circles the center.
And because it can be centered. The entrance takes place on the 3rd ring and the center is reached from the 5th ring. This also creates a small empty space.

I also like the rhythm, it is reminiscent of that of the Chartres labyrinth. It goes quickly to the middle and then follows the long walking in all sectors. Pretty much at the end you come back very close to the entrance, circle the entire labyrinth and then quickly get to the center.

An inverted pentagram is drawn in the middle in Gossembrot’s handwriting. I tried to fully integrate that. The top of the star points down. It is oriented in the direction of the 5 axes. Gossembrot designed the labyrinth around 1480. So this arrangement has no satanic character at all. These ideas only appeared in the middle of the 19th century.

I expressly recommend the excellent article on Wikipedia (see link below) about the geometry and meaning of the pentagram.

The dual and centered labyrinth type Gossembrot 51 r in Knidos style

The five axes also tempt you to choose a pentagonal layout. The same widths for the lines (in black) and the paths (in white) and the angular edges also give it a spatial effect.

The dual labyrinth type Gossembrot 51 r centered in pentagonal shape

Ariadne’s thread in the dual labyrinth type Gossembrot 51 r centered in pentagonal shape

The effect is spatial, but it seems to go deeper.

Who dares to build such a labyrinth as a walkable labyrinth?
As far as I know there is not a single copy worldwide. It looks new and modern, but its origins go back over 500 years.
The star in the middle, on the other hand, could be left out or only slightly indicated. It is not an element in the type, but is part of the style, similar to the six “petals” in the Chartres labyrinth.
An empty center is always inviting and open to a wide variety of applications.

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# The Relatives of the Labyrinth Type Gossembrot 51 r

The labyrinth on folio 51 r is Gossembrot’s most important one. It is the earliest preserved example of a five-arm labyrinth at all. It’s course of the pathway using double barriers in all side-arms is unprecedented (see: related posts 1, below). However, it is not self-dual. Therefore, it can be expected that there exist three relatives of it (related posts 4).

I term as relatives of an (original) labyrinth the dual, complementary, and dual-complementary labyrinths of it (related posts 2 and 3). In fig. 1 the patterns of the Gossembrot 51 r-type labyrinth (a, original), the dual (b), the complementary (c), and the dual-complementary (d) of it are presented.

Figure 1. Patterns of the Relatives of Type Gossembrot 51 r

Figure 2 shows the labyrinths corresponding to the patterns in their basic form with the walls delimiting the pathway on concentric layout and in clockwise rotation.

Figure 2. The Relatives of Type Gossembrot 51 r in the Basic Form

These four related labyrinths all look quite similar. To me it seems, the dual (b) and the complementary (c) look somewhat less balanced than the original (a) and the dual-complementary (d). Presently, I am not aware of any existing examples of a relative to the Gossembrot 51 r-type labyrinth.

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