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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