Labyrinths with Pseudo Single-Barriers 

In my last post I have introduced the pseudo single-barrier, presented the two only historical labyrinths with pseudo single-barriers I am aware of, and have shown an own labyrinth with 2 axes, 3 circuits and one pseudo single-barrier (see: related posts, below).

The pattern for this labyrinth with 2 axes and 3 circuits can be easily enlarged, such that labyrinths with multiple axes and exclusively containing pseudo single-barriers can be designed. Figure 1 shows a labyrinth with 3 axes and 5 circuits with 2 pseudo single-barriers. 

Figure 1. Labyrinth with 3 Axes and 5 Circuits
Figure 1. Labyrinth with 3 Axes and 5 Circuits

In fig. 2, a labyrinth with 4 axes, 7 circuits and 4 pseudo single-barriers is presented. 

Figure 2. Labyrinth with 4 Axes and 7 Circuits
Figure 2. Labyrinth with 4 Axes and 7 Circuits

Figure 3, finally, shows a labyrinth with 5 axes, 9 circuits and 8 pseudo single-barriers. 

Figure 3. Labyrinth with 5 Axes and 9 Circuits
Figure 3. Labyrinth with 5 Axes and 9 Circuits

All pseudo single-barriers are situated in the side axes. Furthermore, they are placed such, that the pathway always in its movement forward skips two circuits from the outside in without changing its direction. In the movement backward, the pathway follows a serpentine pattern. 

This pattern can be extended so that labyrinths with any desired number of axes with pseudo single-barriers can be generated. 

Related Post:

Pseudo Single Barrier

As was the case with double-barriers, we can also distinguish real from pseudo single-barriers (see: related posts, below). Here I want to show this first with the examples of two non-labyrinthine figures. I start with the figure „Luan“ (fig. 1).

Figure 1. Figure Luan
Figure 1. Figure “Luan” 

Source: Kern, fig 604, p. 285

This is a recent sand drawing of the Stone Age culture on Melanesian island Malekula (Vanatu). Kern writes, that this figure is not a labyrinth and cannot not even with any sound justification be considered misinterpreted labyrinth (Kern, p. 285). It is made-up of a uninterrupted line without entrance or center. However, it has 4 axes and 5 circuits. 

In fig. 2, left image, I show a simpler version of it with only 3 circuits. This better illustrates the principle of its design. This figure clearly can be read as an uninterrupted Ariadne’s Thread, and therefore I have drawn it in red. Of course, we can also add the representation with the walls delimiting the pathway (right image, blue). As can be seen, this figure has a certain similarity with a labyrinth. The axes are formed by the same turns of the pathway that typically appear in the labyrinth of Chartres and many other types of labyrinths. 

Figure 2. Figure Luan, Reduced to 3 Circuits
Figure 2. Figure “Luan”, Reduced to 3 Circuits

In figure 3, I have redrawn the figure from fig. 2 and reduced it to 2 axes. The left (red) image shows the representation with the Ariadne’s Thread, the right (blue) shows the representation with the walls delimiting the pathway. Still, the Ariadne’s Thread is a uninterrupted line without entrance or center. Here we can see the special course of the pathway at the side axis. The two turns of the path are shifted one circuit against each other. In between, an axial piece of the pathway is inserted where the path changes from the first to the third circuit without changing direction. Analogically with the double barriers we can term these courses single barriers. The course of the pathway in figure 2 is a real, the one in fig. 4 a pseudo single barrier (see related posts, below). 

Figure 3. Redrawing with 2 Axes and Pseudo Single Barriers
Figure 3. Redrawing with 2 Axes and Pseudo Single Barriers 

This figure can easily be transformed to a labyrinth with 2 axes and 3 circuits, as shown in fig. 4. The left (red) image shows the representation of the labyrinth with the Ariadne’s Thread, the right (blue) shows the representation with the walls delimiting the pathway. 

Figure 4. Labyrinth with 2 Axes and 3 Circuits
Figure 4. Labyrinth with 2 Axes and 3 Circuits

As far as I know, the pseudo single-barrier has appeared in two historical labyrinths (fig. 5). The left image shows the pavement labyrinth in Ely Cathedral with 5 axes and 5 circuits. The pseudo single-barrier is situated at the second axis where the path changes from the fourth to the second circuit without changing direction. The right image shows the third out of 8 labyrinth drafts by the clergyman Dom Nicolas Rély. This labyrinth, that I called Rély 3, has 9 axes and 5 circuits. The axes are designed as real (axes 1, 2, 4, 6, 8) and pseudo (axes 3, 5, 7) single-barriers.

Figure 5. Historical Labyrinths with Pseudo Single Barriers
Figure 5. Historical Labyrinths with Pseudo Single Barriers

Sources: Ely – Saward, p. 115; Rély 3 – Kern, fig. 457a, p. 241.

References:

  • Kern H. Through the Labyrinth: Designs and Meanings over 5000 years. London: Prestel 2000. 
  • Saward J. Labyrinths & Mazes: The Definitive Guide to Ancient & Modern Traditions. London: Gaia 2003.

Related Post:

How to sort a Labyrinth Group

Where does a labyrinth belong? And what relatives does it have? How do I actually sort the related labyrinths in a group? What kind of relationships are there? Or: How do I find the related ones in a group?

If I want to know something more, I first take an arbitrary labyrinth and generate the further relatives of a group by counting backwards and completing the numbers of the circuit sequences. It doesn’t matter whether I “catch” the basic labyrinth by chance or any member of the group.

As an example, I’ll take the 11 circuit labyrinth chosen as the second suggestion in my last post. Here it can be seen in a centered version in Knidos style:

11 circuit Classical 7_9 Labyrinth
11 circuit Classical 7_9 Labyrinth

The level sequence is: 0-7-2-5-4-3-6-1-8-11-10-9-12. The entrance to the labyrinth is on the 7th circuit, the entrance to the center is from the 9th circuit. This is the reason to name it 7_9 labyrinth.

By counting backwards (and swapping 0 and 12), I create the transpose labyrinth to it: 0-9-10-11-8-1-6-3-4-5-2-7-12.

11 circuit Classical 9_7 Labyrinth
11 circuit Classical 9_7 Labyrinth

The entrance to the labyrinth is on the 9th circuit, and the entrance to the center is on the 7th circuit.

Now I complete this circuit sequence 9-10-11-8-1-6-3-4-5-2-7 to the number 12 of the center, and get the following level sequence: 0-3-2-1-4-11-6-9-8-7-10-5-12. This results in the corresponding complementary version.

11 circuit Classical 3_5 Labyrinth
11 circuit Classical 3_5 Labyrinth

Now a labyrinth is missing, because there are four different versions for the non-self-dual types.
The easiest way to do this is to count backwards again (so I form the corresponding transpose version) and get from the circuit sequence 0-3-2-1-4-11-6-9-8-7-10-5-12 the circuit sequence: 0-5-10-7-8-9-6-11-4-1-2-3-12.
Alternatively, however, I could have produced the complementary copy by completing the digits of the path sequence of the first example above to 12.

11 circuit Classical 5_3 Labyrinth
11 circuit Classical 5_3 Labyrinth

The entrance to the labyrinth is made on the 5th circuit, and the entrance to the center is made from the 3rd circuit.


Now I have produced many transpose and complementary copies. But which is the basic labyrinth and which the dual? And the “real” transpose and complementary ones?

Sorting is done on the basis of the circuit sequences. The basic labyrinth is the one that starts with the lowest digit: 0-3-2-1-4-11-6-9-8-7-10-5-12, in short: the 3_5 labyrinth, i.e. our third example above.

The next is the transpose, the 5_3 labyrinth, the fourth example above.

This is followed by the dual, the 7_9 maze, which is the first example above.

The fourth is the complementary labyrinth, the 9_7 labyrinth, the second example above.

The order is therefore: B, T, D, C. This is independent of how the labyrinth was formed, whether by counting backwards or by completing the circuit sequences.

To conclude a short excerpt from the work of Yadina Clark, who is in the process of working out basic principles about labyrinth typology:

Groups

Labyrinths related by Base-Dual-Transpose-Complement relationships

Any labyrinth in a group can be chosen as the base starting point to look at these relationships, but the standard arrangement of the group begins with the numerically lowest circuit sequence string in the base position.

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Christmas 2021

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

Christmas tree labyrinth
Christmas tree labyrinth

This type of labyrinth has already been described on this blog (see below). Now it should serve as a Christmas tree labyrinth in a triangular shape.

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