# 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.

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

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

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.

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# Self-dual Labyrinths with even Numbers of Circuits

In labyrinths with even numbers of circuits, there are usually only two relatives, the base labyrinth and the dual (see: related posts, below). Here, I want to present another labyrinth with an even number of circuits and show, that first the calculation of the relatives also works in labyrinths with more axes than one and, second, show what results in a self-dual labyrinth with an even number of circuits. For this, I use a small labyrinth with two axes in order not to let the sequence of circuits grow too long.

In fig. 2, I perform the calculation following the usual method. The result is, that the transpose and the complementary sequences of circuits are the same. Both also result in the same figure, that is no labyrinth. In this figure, the pathway does not reach the center but ends in a dead-end.

If we write the complementary sequence of circuits in reverse order or complement the transpose sequence of circuits at each position to 7, we obtain the dual sequence of circuits. This is the same as the base sequence.

In labyrinths with even numbers of circuits, the group, thus, has only two members: the base labyrinth and the dual, or only one member in cases of self-dual labyrinths.

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# The Relatives of the Ravenna-type Labyrinth

Among labyrinths with mulitple arms it is also common that one labyrinth is interesting and the complementary to it is uninteresting. An example for this is the labyrinth of the type Ravenna (figure 1).

Figure 1. The Labyrinth of Ravenna

This labyrinth has 4 arms and 7 circuits. The pathway enters it on the innermost circuit and reaches the center from the fifth circuit. It is, thus, an interesting labyrinth. This type of labyrinth has been named after the example laid in church San Vitale from Ravenna. What is really special in this example is the graphical design of the pathway. This is designed by a sequence of triangles pointing outwards. The effect is, that the direction from the inside out is strongly highlighted. This stands in contrast to the common way we use to approach a labyrinth and seems just an invitation to look up the dual of this labyrinth. Because the course of the pathway from the inside out of an original labyrinth is the same as the course from the outside into the dual labyrinth.

I term as relatives of an original labyrinth the dual, complementary, and complementary-dual labyrinths of it. In fig. 2 the patterns of the Ravenna-type labyrinth (a, original), the dual (b), the complementary (c), and the complementary-dual (d) of it are presented.

Figure 2. The Relatives of the Ravenna-type Labyrinth – Patterns

The original (a) and the dual (b) are interesting labyrinths. The complementaries of them are uninteresting labyrinths, because in these the pathway enters the labyrinth on the outermost circuit (c) or reaches the center from the innermost circuit (d). The dual of an interesting labyrinth always is an interesting labyrinth too, the dual of an unintersting is always uninteresting labyrinth too.

Figure 3 shows the labyrinths corresponding to the patterns in their basic form with the walls delimiting the pathway on concentric layout and in clockwise rotation. Presently, I am not aware of any existing examples of a dual (b), complementary (c) or complementary-dual (d) to the Ravenna type labyrinth (a).

Figure 3. The Relatives of the Ravenna-type Labyrinth – Basic Forms

From these basic forms it can be well seen that it seems justified to classify the complementary and complementary-dual labyrinths as uninteresting. The outermost (labyrinth c) and innermost (labyrinth d) respectively walls delimiting the path appear disrupted. Therefore labyrinths c and d seem less perfect than the original (a) and dual (b) labyrinths, where the pathway enters the labyrinth and reaches the center axially.

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# The New Labyrinth in the Church Mariä Schutz on the Vogelsburg at Volkach an der Mainschleife (Germany)

There is now a new labyrinth at this extraordinary and historically significant place.

In the church Mariä Schutz a labyrinth was built during the three-year period of renovation and rebuilding on the area of the Vogelsburg.
Father Bernhard Stühler, hospital chaplain of the Juliusspital, initiated it. Architect Stephan Tittl from the office SequenzSieben Würzburg made the architectural design of the church and delivered the layout. During the inauguration of the project turned out, that Sr. Hedwig Mayer, prioress of the Augustinusschwestern on the Vogelsburg, always had wished a labyrinth.

The new labyrinth

It’s a newly created sector labyrinth with 5 circuits. In the middle is a bowl-shaped pitch circle to divert the direction. The dividing bars form a cross and are arranged symmetrically.
The diameter amounts to 6 m, the middle to 2 m. The ways are 34 cm wide and are marked by a 6 cm wide brass sheet on the terrazzo floor. The way into the center amounts to about 64 m.

One enters the church from the south over an outside stair. On the left hand of the entrance is the labyrinth which is aligned to the west and the east. You enter it from the west, arriving the center, one looks to the east in the direction of the altar and leaves it also again in this direction.

The Oberpflegeamtsdirektor (Chief Administrative Officer) Walter Herbert of the Juliusspitalstiftung (foundation Juliusspital) said on occasion of the inauguration of the altar in May, 2016 to the interior design of the church:

With the elected interior design and with the labyrinth in the ground we would like to offer to every visitor of the Vogelsburg the possibility to find the way to one’s own center, to get back to basics and to find the possibility of steering towards God in the church space.

The segments of the 5 circuits

As Andreas proposed in his last article we can number the 20 segments for the 5 circuits in this 4-armed labyrinth. The sequence of segments can be derived from it for the pathways. Some segments form a connected section which runs through several quadrants. These segments can be marked by brackets. The sequence of segments then looks as follow: 9-5-(1-2-3-4)-8-12-(16-15)-11-(7-6)-10-(14-13) – (17-18-19-20)-21. I write the result a little bit differently than Andreas and still add the center at the end. Inside this labyrinth we have as a specific feature two segments which enclose the full length of a circuit.

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