Sigmund Gossembrot / 5

The Two One-arm Labyrinths

Among the nine drawings by Gossembrot are also two one-arm labyrinths (see related posts, below).

The labyrinth on fol. 53 r has 9 circuits (fig. 1). In the center is written: inducens et educens, leading in and leading out. The design of the axis with it’s rhombus shape is eye-catching.
This almost looks a bit like an anticipation of the Knidos style… Furthermore, this is a non-alternating labyrinth. The pathway traverses the axis when changing from the 6th to the 9th circuit. I have highlighted this position in the labyrinth with two dashed red lines. To these correspond the dashed lines in the pattern. This pattern appears for the first time in the labyrinth by Gossembrot. Therefore it is a type of it’s own. I refer to it as type Gossembrot 53 r.

Figure 1. The Labyrinth on Folio 53 r

The labyrinth on fol. 54 v has 11 circuits and is designed in the concentric style (fig. 2). This type of labyrinth is also referred to as the scaled-up basic type or scaled-up classical / Cretan type of labyrinth. This, because the seed pattern in the classical style consists of a central cross with two nested angles and a coaxial bullet point between each two arms of the cross. The seed pattern of the basic type is made-up of a central cross with one angle and bullet point between each two arms of the cross.

Figure 2. The Labyrinth on Folio 54 v

There exist several historical examples of this type of labyrinth. The two earliest examples (fig. 3) are frescos in the church of Hesselager, Fünen, Denmark and in the church of Sibbo, Finnland (see literature, below).

Figure 3. Earliest Historical Examples (15 th Century)

Both were dated from the 15 th century without any further precision. Also, Gossembrot 54 v dates from the 15 th century (1480). Therefore, based on the dating, it is not possible to certainly identify the earliest preserved example of this type of labyrinth. So it is even conceivable, that the drawing by Gossembrot is earliest and thus Gossembrot was also the originator of this type of labyrinth.

Literature
Kern H. Through the Labyrinth – Designs and Meanings over 5000 Years. München, London, New York: Prestel 2000. P. 280, fig. 593; p. 281, fig. 601.

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Where there are no Complementary Labyrinths

It is not possible to design a complementary counterpart for each labyrinth. The complementary is obtained by horizontally mirroring of the pattern whilst the connections between the entrance, the center and their corresponding circuits in the labyrinth are left uninterrupted. If the entrance and the access to the center are situated on the same side of the axis, this does not work.

Figure 1. Alternating Labyrinth with an even Number of Circuits

Fig. 1 shows this with the example of the alternating, one-arm labyrinth with 6 circuits and the sequence of circuits 3 2 1 6 5 4. As can be seen from the pattern (figure in the middle), the entrance and the access to the center are situated on the same side of the axis. The pathway first leads to the 3rd cricuit and finally reaches the center from the 4th circuit. If we want to mirror this pattern and let the connections with the entrance and the center unbroken, then the lines intersect at the position marked with a black circle. Such a figure is not free of crossroads any more and thus no labyrinth. In alternating labyrinths with an even number of cirucits, therefore, there exist no complementary labyrinths.

Now there are also non-alternating labyrinths with an even number of circuits in which the entrance to the labyrinth and the access to the center lie on the opposite sides of the axis. The labyrinth shown in fig. 2 is such an example and has already been repeatedly discussed in this blog.

Figure 2. Non-alternating Labyrinth with an even Number of Circuits

This non-alternating, one-arm labyrinth with 6 circuits has the sequence of circuits 3 2 1-6 5 4. That is the same sequence of cirucits as in labyrinth shown in fig. 1 with the difference, that the pathway traverses the axis between circuit 1 and 6. So we are here presented a labyrinth with an even number of circuits, but with the entrance and access to the center on the opposite sides of the axis. Despite this, it is not possible to form a complementary labyrinth to this. If we mirror the pattern vertically without interrupting the connections with the entrance and the center, this results in two crossroads (highlighted with black circles).

Thus, complementary counterparts can only be found in alternating labyrinths with an odd number of circuits.

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The Labyrinth by Al Qazvini

An interesting labyrinth is reproduced in the book of Kern (fig. 200, p. 119)°. A drawing by Arabian geographer Al Qazvini in his cosmography completed in 1276 is meant to show the ground plan of the residence of the ruler of Byzantium, before the large city of Constantinople was built up.

This non-alternating labyrinth has 10 circuits and a unique course of the pathway. I will show this using the Ariadne’s Thread and the pattern. In my post “From the Ariadne’s Thread to the Pattern – Method 2” (see related posts, below), I have already described how the pattern can be obtained. When deriving the pattern I always start with a labyrinth that rotates clockwise and lies with the entrance from below. The labyrinth by Qazvini rotates in clockwise direction, however it lies with the entrance from above. Therefore I rotate the following images of the labyrinth by a semicircle so that the entrance comes to lie from below. So it is possible to follow the course of the pathway with the Ariadne’s Thread and in parallel see how this is represented in the pattern.

Four steps can be distinguished in the course of the pathway.

Phase 1

The path first leads to the 3rd circuit. The entrance is marked with an arrow pointing inwards. In the pattern, axial sections of the path are represented by vertical, circuits by horizontal lines. The way from the outside in is represented from above to below.

Phase 2

In a second step, the path now winds itself inwards in the shape of a serpentine until it reaches the 10th and innermost circuit. Up to this point the course is alternating.

Phase 3

Next follows the section where the pathway leads from the innermost to the outermost circuit whilst it traverses the axis. In order to derive the pattern, the labyrinth is split along the axis and then uncurled on both sides. As the pathway traverses the axis, the piece of it along the axis has to be split in two halves (see related posts below: “The Pattern in Non-alternating Labyrinths”). This is indicated with the dashed lines. These show one and the same piece of the pathway. In the pattern, as all other axial pieces, this is represented vertically, however with lines showing up on both sides of the rectangular form and a course similarly on both sides from bottom to top.

Phase 4

Finally the pathway continues on the outermost circuit in the same direction it had previously taken on the innermost circuit (anti clockwise), then turns to the second circuit, from where it reaches the center (highlighted with a bullet point).

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°Kern, Hermann. Through the Labyrinth – Designs and Meanings over 5000 Years. Munich: Prestel, 2000.

Sequence of Segments in One-arm Labyrinths

With the coordinates for segments from the last post (see related posts below) we have now found an understandable notation for the sequence of segments of labyrinths. Here it seems important to me to add that such coordinates can also be used for one-arm labyrinths. I will show this with the examples for which I had already shown the sequences of circuits (see related posts). For this, each circuit has to be divided into two segments.

Partitioning of Circuits in Segments

Next we write the sequences of segments for the three examples and also compare them straightaway with their sequences of circuits.

 

 

A unique notation for one-arm labyrinths can also be achieved, if we can write two different numbers on the same circuit, one for each side of the axis. For this, the circuits have to be partitioned into two segments. This allows us to write unique sequences of segments for alternating and non-alternating labyrinths. Also it is possible to use the same form of notation in one-arm and multiple-arm labyrinths. However, this notation will always need 14 coordinates for each one-arm labyrinth with 7 circuits. This is clearly more digits than are needed for the sequences of cirucits with separators.

 

 

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