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.
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.
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.