Labyrinth for the New Year 2023

Crossing Labyrinth with 4 Axes and 10 Circuits. Self-dual. Own Design.
Crossing Labyrinth with 4 Axes and 10 Circuits. Self-dual. Own Design.
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The Crossing Labyrinths by Dom Nicolas de Rély

The last crossing labyrinths I want to show were all designed by Dom Nicolas de Rely. This clergyman from Benedictine abbey Corbie near Amiens has produced eight drawings with own labyrinth designs, all in pen and ink. Three of them are crossing labyrinths. I have ordered them by the number of axes and labelled them Rely 2, 3, and 4. 

Rély 2 has 15 circuits. It is designed on a layout with 8 axes; however by shifting of one (real) single barrier, it can be reduced to 7 axes. The pathway crosses the main axis from the 7th to the 12th circuit. And it reaches the center from the innermost 15th circuit, which is a complete attached trivial circuit. Therefore it is an uninteresting labyrinth (fig. 1). 

Figure 1. Rély 2
Figure 1. Rély 2

Because of its pseudo single barriers, Rely 3 has been already shown on this blog (see related posts, below). It has 9 axes and 5 circuits. The pathway crosses the main axis from the 4th to the 1st circuit and reaches the center after a full circle on an attached trivial 5th circuit. Thus, also this labyrinth has to be described as uninteresting (fig. 2).

Figure 2. Rély 3
Figure 2. Rély 3

The third crossing labyrinth, Rély 4, is designed on a layout with 14 axes and 15 circuits (fig. 3). This, however, can be reduced to 10 axes. The pathway crosses the main axis from the 6th to the 13th circuit. The entrance to the labyrinth is from the left side and (erroneously?) closed. The center is not reached at the main axis, but from the third side-axis on the innermost circuit. Therefore there remains a short piece of the pathway leading into a dead-end at the end of the last circuit.

Figure 3. Rély 4
Figure 3. Rély 4

I will have a closer look at the two labyrinths Rély 2 and Rély 4 in a later post.

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Reflections on the Wunderkreis, 2

As we have seen (in part 1), the most different variants of the Wunderkreis can be created. Depending on which part is emphasized more or less, they then look like.
When creating a new labyrinth, of course, it also depends on the size of the available space and the purpose the labyrinth is to serve.

Type 5 a-c
Type 5 a-c

The path sequence, if we go first to the left: 0-3-2-1-4-a1-b2-c1-c2-b1-a2-5-0. To the right we have: 0-5-a2-b1-c2-c1-b2-a1-4-1-2-3-0.
With the digits we have the sequence with odd and even numbers, as we know it from a classical labyrinth.
With the letters, which designate the elements of the double spiral, we can also see a certain systematic: The letters come alternately one after the other. If two identical letters follow each other, we have reached the center of the spiral and the basic change of direction. The additions “1” designate the lower part and the addition “2” the upper part of a transition.
If we take a closer look at the circuit sequences, we can see that the second one (to the right) is opposite to the first one.
So we can say that here two different but related labyrinths of a group are united in one. Depending on which path we choose first.

How many circuits does this Wunderkreis actually have?
That is a little difficult to count. To do this, we divide the figure into three parts, the lower left quarter, the upper half, and the lower right quarter. Let’s start at the bottom left: There are the 3 “labyrinthine” circuits and 3 of the double spiral. At the top we have 4 “labyrinthine” circuits and the 3 of the double spiral. Bottom right: 5 “labyrinthine” circuits and the 3 of the double spiral. So, depending on the angle of view, we have 6, 7 or 8 circuits.
The type designation is the maximum number of “labyrinthine” turns plus the letter sequence for the turns of the double spiral. Adding both gives the number of total circuits. In this example “5 a-c” so 8 in total.
In the file name for the drawings I have tried to express this as well, additionally provided with the indication of the entrance and the exit of the labyrinth.

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