The Luan Labyrinth

Andreas recently brought into play the sand drawing “Luan” on Malekula, which Hermann Kern rejected as a labyrinth. It represents an uninterrupted line, but without an entrance or an access to the center.

Figure 1. Figure Luan
Figure 1. Figure “Luan”

But it attracted me to try to make a “real” labyrinth out of it. To do this, there must be a beginning and an end. This is easily done by cutting the unbroken line at one point. And then you bend the end piece towards the center. I took the lowest point of the outer line.

This is how the drawing will look as a labyrinth figure in concentric form:

The 5-circuit Luan Labyrinth
The 5-circuit Luan Labyrinth

The figure may look quite different from the original at first glance, but the lines are identical. The labyrinth has five circuits and four axes with three double barriers and passes through four sectors. The entrance to the labyrinth is on the first circuit, as is the entrance to the center. The path moves in serpentines towards and away from the center. It is a sector labyrinth and is reminiscent of the Roman labyrinths in serpentine form.

From a design point of view, I don’t really like the entrance to the labyrinth on the first circuit. By the way, an entrance to the center from the last circuit is not very happy either. Both are often seen in newly designed labyrinths.
How can this be changed? The easiest way to do this is to choose only two double barriers instead of three, thus obtaining three sectors.

This is how it looks then:

The 5-circuit, 3-axle Luan Labyrinth
The 5-circuit, 3-axle Luan Labyrinth

The entrance to the labyrinth is on the 5th circuit and the entrance to the center is again from the 1st circuit as in the four-axis labyrinth.

Now we want to work a bit more on the reshaping. What would it look like if I arranged only 3 circuits instead of the 5?

The 3-circuit Luan Labyrinth
The 3-circuit Luan Labyrinth

Now this is very reminiscent of labyrinths shown earlier in this blog (see related posts below), especially the 3 circuit Chartres labyrinth.

Very topically to this Denny Dyke offers a necklace with pendant with exactly this labyrinth on his website:

Necklace from Circles in the Sand
Necklace from Circles in the Sand

This shows once again how interesting the subject of labyrinths can be.

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How to sort a Labyrinth Group

Where does a labyrinth belong? And what relatives does it have? How do I actually sort the related labyrinths in a group? What kind of relationships are there? Or: How do I find the related ones in a group?

If I want to know something more, I first take an arbitrary labyrinth and generate the further relatives of a group by counting backwards and completing the numbers of the circuit sequences. It doesn’t matter whether I “catch” the basic labyrinth by chance or any member of the group.

As an example, I’ll take the 11 circuit labyrinth chosen as the second suggestion in my last post. Here it can be seen in a centered version in Knidos style:

11 circuit Classical 7_9 Labyrinth
11 circuit Classical 7_9 Labyrinth

The level sequence is: 0-7-2-5-4-3-6-1-8-11-10-9-12. The entrance to the labyrinth is on the 7th circuit, the entrance to the center is from the 9th circuit. This is the reason to name it 7_9 labyrinth.

By counting backwards (and swapping 0 and 12), I create the transpose labyrinth to it: 0-9-10-11-8-1-6-3-4-5-2-7-12.

11 circuit Classical 9_7 Labyrinth
11 circuit Classical 9_7 Labyrinth

The entrance to the labyrinth is on the 9th circuit, and the entrance to the center is on the 7th circuit.

Now I complete this circuit sequence 9-10-11-8-1-6-3-4-5-2-7 to the number 12 of the center, and get the following level sequence: 0-3-2-1-4-11-6-9-8-7-10-5-12. This results in the corresponding complementary version.

11 circuit Classical 3_5 Labyrinth
11 circuit Classical 3_5 Labyrinth

Now a labyrinth is missing, because there are four different versions for the non-self-dual types.
The easiest way to do this is to count backwards again (so I form the corresponding transpose version) and get from the circuit sequence 0-3-2-1-4-11-6-9-8-7-10-5-12 the circuit sequence: 0-5-10-7-8-9-6-11-4-1-2-3-12.
Alternatively, however, I could have produced the complementary copy by completing the digits of the path sequence of the first example above to 12.

11 circuit Classical 5_3 Labyrinth
11 circuit Classical 5_3 Labyrinth

The entrance to the labyrinth is made on the 5th circuit, and the entrance to the center is made from the 3rd circuit.


Now I have produced many transpose and complementary copies. But which is the basic labyrinth and which the dual? And the “real” transpose and complementary ones?

Sorting is done on the basis of the circuit sequences. The basic labyrinth is the one that starts with the lowest digit: 0-3-2-1-4-11-6-9-8-7-10-5-12, in short: the 3_5 labyrinth, i.e. our third example above.

The next is the transpose, the 5_3 labyrinth, the fourth example above.

This is followed by the dual, the 7_9 maze, which is the first example above.

The fourth is the complementary labyrinth, the 9_7 labyrinth, the second example above.

The order is therefore: B, T, D, C. This is independent of how the labyrinth was formed, whether by counting backwards or by completing the circuit sequences.

To conclude a short excerpt from the work of Yadina Clark, who is in the process of working out basic principles about labyrinth typology:

Groups

Labyrinths related by Base-Dual-Transpose-Complement relationships

Any labyrinth in a group can be chosen as the base starting point to look at these relationships, but the standard arrangement of the group begins with the numerically lowest circuit sequence string in the base position.

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Christmas 2021

Wishing all visitors of this blog a Merry Christmas and a Happy New Year!

Christmas tree labyrinth
Christmas tree labyrinth

This type of labyrinth has already been described on this blog (see below). Now it should serve as a Christmas tree labyrinth in a triangular shape.

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How to Make an Aligned Wunderkreis

I have already explained the principle some years ago. In the meantime I have gained some knowledge about it, so that I can once again present a proposal for a construction method. This applies to both the drawing and a stakeout on site using simple surveying tools.

I present a prototype based on an axial dimension of one meter. This allows the Wunderkreis to be scaled to any desired scale.

We start with a basic framework with the definition of an axis, on which the input axis is to be placed here. That would be the line E-C. It runs centrally between the midpoints M3 and M4.
After defining the points A, E and B, the center point M3 can be defined by arcs. And from there, the other centers M2, M1 and M4 can be determined.

Note for experienced surveyors:
Right-angled (Cartesian) coordinates can be determined from the horizontal and vertical dimension chains. With appropriate measuring instruments, the most important main points can then also be polar staked out.

However, the radii themselves are best marked out with a line, wire or tape measure and marked with spray paint, sawdust or bark mulch.

Wunderkreis: construction elements
Wunderkreis: construction elements

It makes sense to mark out the upper semicircles (shown here in gray) around the center point M4. Then the four semicircles around the center point M3, as well as the left (5) and right (7) arc pieces (shown in green). The semicircles (drawn in gray) around the centers M1 and M2 form the final part.

Wunderkreis: radii
Wunderkreis: radii

Depending on the design of the boundary lines (according to the width) the Wunderkreis looks like. Shortly after entering the entrance below there is a branch. If one goes to the left, one walks first through the outer circuits. After passing through the inner double spiral, one gets back to the beginning.

We have a so-called walk-through or procession labyrinth before us. There is no strictly defined center.

Ariadne's Thread inside the Wunderkreis
Ariadne’s Thread inside the Wunderkreis

The following drawing once again shows all the necessary construction elements and the corresponding lines for the walls and the path (in red, Ariadne’s thread).

Layout drawing of the Wunderkreis
Layout drawing of the Wunderkreis

Here is the drawing as a PDF file for printing, saving or viewing.
To do this, go to the three points in the top right of the document

The PDF file of the layout drawing for the Wunderkreis

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