From Meander to Labyrinth

Hermann Kern is writing in his book Through the Labyrinth (Prestel Verlag, Munich) on page 23 about the principles of form:

Every labyrinth consists of lines that may be construed as a sort of ground plan; they form a sophisticated pattern of movement that requires considerable powers of the imagination to grasp. By trying to envisage walking the path between the lines, one can begin to comprehend this pattern.

Quoting this, I don’t want to deter someone, but make clearly that the employment with the labyrinth can be absolutely demanding. And I would like to assist for a better understanding.

From all one can “generate” a labyrinth, more exactly said: the way in a labyrinth. Since the meander is Ariadne’s thread (just the way) in linear form.
On looking more carefully one recognises some small differences. They are formed by mirroring the “basic form” either in horizontal or vertical axis. One can distinguish four different variations. In the following drawing this can be understood with the help of the colours and figures:

I can “read” the meander from left to right or from right to left. Accordingly to that is the situation of the entrance.

How do I make a labyrinth out of the meander? Or said a little more sophisticated: What code is hidden in the meander that leads me to the labyrinth?

I try to make the “deciphering” as easily comprehensible as possible. Therefore the colours and the figures shall serve as help. So one can pursue the way of the single segments.

Rotated meander

Rotated meander

First I turn the meander with the access below left from the above drawing about 90 degrees to the left.
The “secret” in the meander is the arrangement of the lines. They are numbered from “0” to “8”. “0” stands for outside, beginning of the line, init. “8” stands for inside, end of the line, middle, center, goal, target, aim. These line segments are also marked with different colours.
Now I read the order in which these segments will be passed through. And, true readers of this blog know it, this will give me the path sequence (line sequence, circuit sequence, level sequenc) for the labyrinth. It is: 0-3-2-1-4-7-6-5-8.
I can also derive the changes of direction from it. So whether it goes to the left or to the right, outwardly or inwards.

I pull apart this rotated meander crosswise. The labyrinth will be presented as a diagram. Of course the lengths of the single line segments are distorted, do not correspond to the original ones or the new lengths. But it does not depend on it at all. It is only important in which direction a line is running. For it is a pattern. Maybe it is difficultly to understand, above all the situation of the entrance and the center. In the real labyrinth they are situated near together and not as in the pattern on the right or left side outside.

The diagram

The diagram

I imagine this rectangle always as a pulled apart ring or tyre. If I cut the back side of this ring in the middle and lay both outer ends side by side, the entrance will be situated on the left side and the center on the right one.
Maybe one can recognize that better in the lower drawing? If I pursue the numbered lines (3-2-1-4-7-6-5-8) I alternately have to leave one side and enter on the other side again. The best bet is to try out.

The split diagram

The split diagram

Because I can deduce the right path sequence for the labyrinth (Ariadne’s thread) from the meander, I can draw the labyrinth by only using this path sequence. I do not need the well-known seed pattern to draw the labyrinth (the walls).
The labyrinth matching to the meander and the diagram looks as follows:

The left-hand classical labyrinth (Ariadne's thread)

The left-hand classical labyrinth (Ariadne’s thread)

Here in square shape:

The square classical labyrinth

The square classical labyrinth

Which meander generates now this left-hand labyrinth? From the above shown four versions the one with the access below left and the other with the access above right. Why? Because the circuit 3 (yellow) turns to the left after passing through 0 (grey).

However, in the meander versions with the access below right and the access above left circuit 3 turns to the right first. Consequently the labyrinth generated from them must also look different, namely as follows:

The right-hand classical labyrinth (Ariadne's thread)

The right-hand classical labyrinth (Ariadne’s thread)

However, this is nothing else than the vertically mirrored left-hand labyrinth.
Two versions of the classical 7 circuit labyrinth can be derived from the four possible versions of a meander, suitable for a labyrinth.

However, in the end the labyrinth should be also shown in such a way as it many know: With the representation of the boundary lines (the walls). They are held in black. The way, Ariadne’s thread coloured in the drawings before, is the free space between the lines. The boundary lines cross and have a beginning, here even four. This form can be easier generated from the seed pattern.

The left-hand classical labyrinth (walls)

The left-hand classical labyrinth (walls)

If one makes the ways in all circuits of the same width, the usually central cross will change to the the diamond-shaped “fontanel”.

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6 thoughts on “From Meander to Labyrinth

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