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Posts Tagged ‘Compiègne’

The pattern is a transformation of the Ariadnes’s Thread from the closed form into the rectangular form. This is not a labyrinth any more. The exterior of the labyrinth is represented by the area above the pattern, the interior by the area below the pattern. The circuits have transformed to horizontal lines. The arms are all oriented vertically.

AF Demo

Figure 1. The Ariadne’s Thread of my Demonstration Labyrinth

Fig. 1 shows the Ariadne’s Thread of my demonstration labyrinth. In accordance with the direction into the labyrinth, I number the circuits from the outside in. Thus 1 is the outermost, 5 the innermost circuit.

M Demo

Figur 2. The Pattern of my Demonstration Labyrinth

Fig 2 shows how this is represented in the pattern. There, 1 is the uppermost, 5 the lowest horizontal line. In the transformation, the axis is split in a left and right half. These halves come to lie on the left and right outer verticals of the pattern. As long as the pathway follows a circuit, in the pattern this is represented by a horizontal course. When it changes to another circuit, it moves axially and by this forms the axis. In the pattern this is represented vertically. However, this can only be seen clearly in labyrinths with multiple arms.

AF Comp

Figure 3. The Ariadne’s Thread of the Compiègne-Type Labyrinth

Fig. 3 shows the Ariadne’s Thread of the Compiègne labyrinth. This labyrinth has also 5 circuits, but 4 arms. Labyrinths with multiple arms generally are composed of a main axis. This is where the pathway enters the labyrinth and from which it also reaches the center. In addition these labyrinths have one or more side-arms.

First, it has to be made clear, how we want to refer to the arms of the labyrinth. I give the number that corresponds with the number of arms of a labyrinth to its main axis. So, in four-arm labyrinths, I number the main axis with 4. I start the enumeration of the arms with the first side-arm next to the main axis in clockwise direction. The reason for this is, that I always start with the labyrinth orientated such that the entrance is at the bottom and the labyrinth in clockwise rotation when I transform it into the rectangular form.

M Comp

Figure 4. Pattern of the Compiègne-Type Labyrinth

Fig. 4 shows how this affects the pattern. The main axis is split. This is the same as with the only axis in one-arm labyrinths. Both halves of the main axis come to lie at the left and right outer verticals. The side-arms are not split for the transformation. In a four-arm labyrinth, therefore, we can find five vertical lines in the pattern. Two for both halves of the main axis and one for each side-arm. (By the way: I have shifted the labellings of the arms. In the pattern these should lie on top according to the positioning of the labels on the outside of the Ariadne’s Thread, however it reads better this way.)

So, the pattern can be thought as lying on a grid of horizontal and vertical lines. The horizontal lines indicate the circuits, and the path in the pattern follows on these horizontal lines. The vertical lines indicate the arms of the labyrinth. These lie between or aside the turns of the pathway.

What these considerations also show is that we here have read the pattern in one direction. Keep this in mind, it is important.

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I have shown with the example of my demonstration labyrinth how the pattern of a labyrinth can be obtained. This was a one-arm labyrinth. Of course, it is also possible to transform labyrinths with multiple arms into the rectangular form.

Compiegne

Figure 1. Compiègne

I will show this here with the Compiègne labyrinth as an example (fig. 1). This is a labyrinth with four arms. It is presented with the walls shown. Erwin has already used this type of labyrinth in this blog (see related posts). In order to obtain the rectangular form, I will use the Ariadne’s Thread and apply method 2, as usual.

Lage Achsen

Figure 2. The Ariadne’s Thread, situation of the arms

Fig. 2 shows the baseline situation. The labyrinth is represented by the Ariadne’s Thread with the entrance at the base and in clockwise rotation. The main axis and the side-arms are highlighted.

Muster Merhachs Meth2

Figure 3. Flipping the Arms

As can be seen in fig. 3, both side-arms on the left and right side are flipped upwards by about 1/4 of the arc of a circle. There they meet the upper side arm which remains unchanged. Only the main axis is split into two halves, and these are flipped upwards each by ca. Half the arc of a circle, where they attach to the side-arms.

Muster MA Erg2

Figure 4. Finalization of the Pattern

Fig. 4 shows the straightening-out process and, as a result of it, the pattern of the Compiègne labyrinth.

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