Additions to the New Year’s Labyrinth 2021

Today I want to give some more information on the New Year’s Labyrinth of this year. In the caption of the figure, I had indicated that it has 6 axes, 7 circuits and symmetrically arranged single barriers, double barriers and a triple barrier and characterized it as self-transpose (see related posts 1, below). Here I want to explain more in detail what that means. 

Figure 1 shows the pattern of the New Year’s Labyrinth. The axes are numbered. The main axis that is represented on both sides in the pattern, bears number 6. This is not a sector labyrinth. It is made up of two similar halves that are mirrored at the 3rd axis. One could also see in this two superordinated sectors that are composed of 3 segments each. 

Figure 1. Pattern of the New Year's Labyrinth  2021
Figure 1. Pattern of the New Year’s Labyrinth 2021

In fig. 2 the transpose pattern is derived from the pattern (a). For this purpose, first, the pattern has to be mirrored horizontally (against the vertical dashed red line). This results in pattern (b). Mirroring of the pattern interrupts the connections to the exterior (triangle) and to the center (bullet point). The connection lines (grey) point to the wrong direction. In order to reconstruct these connections after the mirroring, second, these two connection lines have to be flipped as indicated with the red arrows. As a result, we obtain in (c) the transpose of pattern (a). What is special in the New Year’s Labyrinth is, that its transpose is the same. Therefore, this labyrinth is referred to as self-transpose. 

Figure 2. Deriving the Transpose Pattern
Figure 2. Deriving the Transpose Pattern

With its six axes, this labyrinth is well suited for a transformation into the Flower-of-Life style (related posts 2). For this, the Ariadne’s Thread is used, as shown in figure 3. 

Figure 3. New Year's Labyrinth in the Flower-of-Life Style
Figure 3. New Year’s Labyrinth in the Flower-of-Life Style

Related Posts

  1. Labyrinth for the New Year 2021
  2. Flower of Life – on Track

The Relatives of the Labyrinth Type Gossembrot 51 r

The labyrinth on folio 51 r is Gossembrot’s most important one. It is the earliest preserved example of a five-arm labyrinth at all. It’s course of the pathway using double barriers in all side-arms is unprecedented (see: related posts 1, below). However, it is not self-dual. Therefore, it can be expected that there exist three relatives of it (related posts 4).

I term as relatives of an (original) labyrinth the dual, complementary, and dual-complementary labyrinths of it (related posts 2 and 3). In fig. 1 the patterns of the Gossembrot 51 r-type labyrinth (a, original), the dual (b), the complementary (c), and the dual-complementary (d) of it are presented.

Figure 1. Patterns of the Relatives of Type Gossembrot 51 r

Figure 2 shows the labyrinths corresponding to the patterns in their basic form with the walls delimiting the pathway on concentric layout and in clockwise rotation.

Figure 2. The Relatives of Type Gossembrot 51 r in the Basic Form

These four related labyrinths all look quite similar. To me it seems, the dual (b) and the complementary (c) look somewhat less balanced than the original (a) and the dual-complementary (d). Presently, I am not aware of any existing examples of a relative to the Gossembrot 51 r-type labyrinth.

Related Posts:

  1. Sigmund Gossembrot / 2
  2. The Relatives of the Wayland’s House Type Labyrinth
  3. The Relatives of the Ravenna Type Labyrinth
  4. The Complementary versus the Dual Labyrinth

Variations on the Babylonian Visceral Labyrinths in Knidos Style

By rotating or mirroring one will get dual and complementary labyrinths of existing labyrinths. Or differently expressed: Other, new labyrinths can be thereby be generated.
So I have three more new labyrinths as I can make a complementary one from a new dual labyrinth and I can make a dual one from a new complementary, which are identical. (For more see the Related Posts below).

Seen from this angle I have examined the still introduced 21 Babylonian Visceral Labyrinths in Knidos style and present here the variations most interesting for me. Since not each of the possible dual or complementary examples seems noteworthy.

Many, above all complementary ones, would begin on the first circuit and lead to the center on the last, which is yet undesirable.

Leaving out trivial circuits also will generate new labyrinths. This applies to the last two ones. If you compare the first and the last example you see two remarkable labyrinths: The first with 12 circuits and the last with 8 circuits, but using the same pattern.

Related Posts

The Complementary Labyrinth

If we turn the inside out of a labyrinth, we obtain the dual labyrinth of it. The dual labyrinth has the same pattern as the original labyrinth, however, the pattern is rotated by a half-circle, and the entrance and the center are exchanged. This has already been extensively described on this blog (see related posts, below).

Now, there is another possibility for a relationship between two labyrinths with the same pattern. In this kind of relationship, the pattern is not rotated, but mirrored vertically. Also – other than in the relationship of the duality – the entrance and the center are not exchanged. At this stage, I term this relation between two labyrinths the complementarity in order to distinguish it from the relationship of the duality.

Here I will show what is meant with the example of the most famous labyrinth.

This labyrinth is the „Cretan“, „Classical“, „Archetype“ or how soever called alternating, one-arm labyrinth with 7 circuits and the sequence of circuits 3 2 1 4 7 6 5, that I will term the „basic type“ from now on.

Figure 1.The Original Labyrinth

Figure 1 shows this type in the concentric style.

The images (1 – 6) of the following gallery (figure 2) show how the pattern of the complementary type can be obtained starting from the pattern of the original type.

Image 1 shows the pattern of the basic type in the conventional form. In image 2 this is drawn slightly different. By this, the connection from the outside (marked with an arrow downwards) into the labyrinth and the access to the center (marked with a bullet point) are somewhat enhanced. This in order to show, that when mirroring the pattern, the entrance and the center will not be exchanged. They remain connected with the same circuits of the pattern. In images 3 til 5 the vertical mirroring is shown, divided up in three intermediate steps. Vertical mirroring means mirroring along a horizontal line. Or else, flipping the figure around a horizontal axis – here indicated with a dashed line. One can imagine, a wire model of the pattern (without entrance, center and the grey axial connection lines) being rotated around this axis until the upper edge lies on bottom and, correspondingly, the lower edge on top. In the original labyrinth, the path leads from the entrance to the third circuit (image 3). With this circuit it remains connected during the next steps of the mirroring (shown grey in images 4, 5 and 6). After completion of the mirroring, however, this circuit has become the fifth circuit.The path thus first leads to the fifth circuit (image 6) of the complementary labyrinth. A similar process occurs on the other side of the pattern. In the original labyrinth, the path reaches the center from the fifth circuit. This circuit remains connected with the center, but transforms to the third circuit after mirroring.

Figure 3: The Complementary Labyrinth

In the pattern of the complementary labyrinth we can find a type of labyrinth that has already been described on this blog (see related posts). It is one of the six very interesting (alternating) labyrinths with 1 arm and 7 circuits. That is to say the one with the S-shaped course of the pathway.

So, what is the difference between the dual and the complementary labyrinth?

Let us remember that the basic type is self-dual. The dual of the basic type thus is a basic type again.

The complementary to the basic type is the type with the S-shaped course of the pathway.

By the way: In this case, the dual to the complementary is the same complementary again, as also the complementary of the basic type is self-dual (otherwise it would not be a very interesting labyrinth).

This opens up very interesting perspectives.

Related posts: