Labyrinth Movement: Wandering in Meanders towards the Middle

The movement figure in a labyrinth is most essential. For me the meander is the most typical movement pattern. The way through the labyrinth is expressed directly by it.

In this post I try to develop different labyrinth types only with this movement pattern. I will not do it from the seed pattern, but directly from the path sequence (cicuit sequence).

The simplest labyrinth has 3 circuits, and appeared first on a coin from Knossos. This is why Andreas calls this the type Knossos. It is made from one meander and has two turning points (beginning and/or end of the walls). The seed pattern for this labyrinth is very simple: Three lines and two dots.

All examples have a square shape with the same width for the walls and the path(Ariadne’s thread). However, they could be as well round or polygonal. The shape plays no role. The movement figure is crucial.
The seed pattern (in blue) is inserted afterwards in the following examples.

The classical 3 circuit labyrinth

The square classical 3 circuit labyrinth type Knossos

There is still an other  3 circuit labyrinth which can be derived from the diminished seed pattern of the classical 7 circuit labyrinth. Nevertheless, it has the path sequence 1-2-3-4 and does not come up as a historical specimen.

In the type Knossos the path sequence is: 3-2-1-4, this is quite an other rhythm. That has to do with the meander.
I would like to stay at this this movement pattern, and continue with it.

Interim result: The 7 circuit classical labyrinth (sometimes called the Cretan type). This is the oldest historically provable labyrinth type which has presumably been developed from the seed pattern for the walls. It is build from two meanders, connected with a additional path. It has four turning points.

The classical 7 circuit labyrinth

The square classical 7 circuit labyrinth

Now we proceed with an other round, and will get with 11 circuits, 6 turning points and 3 meanders the Labyrinth type Otfrid. Here it is square, the “originals” in the historical manuscripts are all round.

The classical 11 circuit labyrinth

The square classical 11 circuit labyrinth type Otfrid

Meanwhile the course of action might be clear: With every new round, we will have four circuits, one meander and two turning points more.

Here the next example:

The classical 15 circuit labyrinth

The square classical 15 circuit labyrinth (new type)

The displayed example is not known as a historical labyrinth. Although there are other 15 circuit labyrinths. Nevertheless, they look different. Since they have been developed from the well-known seed pattern by adding more angles. We find them among the Scandinavian Troy Towns. Andreas calls the 15 circuit Labyrinth type Tibble.

There exist also 11 circuit labyrinths which have been developed from the enlarged seed pattern. Andreas is naming them type Hesselager.

I design the different labyrinth figures out of another idea: By continuing the typical movement of the meander. Only three examples of the so developed labyrinths match with the historical labyrinths which probably have been generated from the seed pattern. So still nobody has presumably had up to now this thought. One can explain with it the labyrinth figure in a new way, and, by the way, create new types.

The next example in this series is a 19 circuit labyrinth:

The classical 19 circuit labyrinth

The square classical 19 circuit labyrinth (new type)

It is a labyrinth with 19 circuits, 5 meanders, and 10 turning points.

One could continue in this style and develop more and more extensive labyrinths. Who like to do that, can do it for oneself.


With this method one can quite simply explain how to draw a labyrinth. Besides, only the paths, Ariadne’ thread, is drawn. Not the walls. If I speak of lines here, the circuits (the path axis) are meant.
Here an example from a kindergarten child:

An 11 circuit classical labyrinth

An 11 circuit classical labyrinth (type Otfrid)

And here the final work of a kindergarten project on the subject labyrinth. Every child has drawn “his” line in this 19 circuit labyrinth.

A 19 circuit labyrinth

A 19 circuit labyrinth (new type)

The next is a personal “attempt to set up a record”. I have stopped at 23 circuits. However, it would be easy to continue. Maybe you try it yourself?

A 23 circuit labyrinth

A 23 circuit labyrinth (new type)

Now I would like to explain here once again the principle. Your best bed would be to reproduce it for yourself on a sheet of paper. Once one knows how to do it, it is quite easy. At the end everybody should be able to draw Ariadne’s thread for the classical 7 circuit labyrinth by heart and in one go.

I would like to describe the movement pattern very simply, possibly in such a way: I encircle the center by moving to the other side. There I turn outwardly and return in parallel equidistant with the just drawn line back to the beginning side. There I repeat this movement: turning outwardly and tracing back to the previous side. There I turn between the up to now drawn lines into the center. The 3 circuit labyrinth would be finished.
However, I can continue instead and change once again to the other side by following the last drawn line. There the process recurs: Again encircling the center by moving to the other side (thereby leaving enough place for two later lines), then turning outwardly and returing back, and repeating the same. Then to the middle and so on.

It is important to remember that the first drawn line forms the third circuit. This means, I must leave enough place for two more lines, which are drawn later. Namely the second  and the first circuit, which are drawn as the second and the third line. This sounds complex, it is maybe also. However, if one has got the hang of it, it is quite easy.

The first 5 lines (circuits) for a square 11 circuit labyrinth

The first 5 lines (circuits) for a square 11 circuit labyrinth

The next 6 lines (circuits) for a square 11 circuit labyrinth

The next 6 lines (circuits) for a square 11 circuit labyrinth

The direction of movement in the previous examples was from the outside inwards. Thereby I can choose any form, a square, a rectangle, a polygon or a circle. I can make angular lines or rounded ones. If I am in the middle, I have finished.

But easily conceivably would be the reverse movement: From the inside outwardly. Then I would have theoretically no more limitation and could make on and on. A change of thinking for the movement would be required also. Best try it yourself.

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Seed Pattern and Pattern

In several previous posts I have shown, that different variants can exist for a certain labyrinth or seed pattern.

KSAF_var

Illustration 1. Variants of the Same Seed Pattern

In Ill. 1 I again show some variants of the seed pattern for the Ariadne’s Thread of my demonstration labyrinth. This same seed pattern can be drawn e.g. with a circular, elliptic, petal-shaped or rectangular outline. The outline figure is only an auxiliary figure. The seed pattern itself is formed by the system of lines within this outline figure. Depending on the shape of the outline figure, also the orientation and rounding of the seeds may somewhat differ. However, they are always ordered the same way. On top left one (not-nested) turn, on bottom left two nested and on the right three nested turns. Which variant of the seed pattern is best suited depends on the purpose for which it is used.

In this post I want to show the relationship between the seed pattern and the pattern. For this purpose, the rectangular variant is best suited. The seed pattern can be transformed to the pattern in a few steps.

KS Umf1

Illustration 2. From Seed Pattern to Meander

The left figure of ill. 2 shows the rectangular variant of the seed pattern. This is also shown as baseline in grey in the right figure. As a first step, the right half of the seed pattern is shifted against the left (shown in red), until it comes to lie on the other side of the left half.

KS Umf2

Illustration 3. From Meander to Pattern

The result of this shift is a meander. It is one of Arnol’d’s figures. This meander is in a next step straightened-out, as has already been shown here. For this, the right half of the seed pattern is shifted somewhat further to the left. The ends opposite each other are then connected with lines.

KS Muster

Illustration 4. Pattern

The result of this process is shown in ill. 4. Apparently, in transforming the meander to the pattern, the first and most important step is the horizontal straightening-out. By this the situation of the circuits in the pattern are made apparent. Next, one can easily straighten-out the axial segments and finalize the pattern.

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A Labyrinth: From the Coffee Cup to a Meadow

Recently I had the following task: To (let) mow a labyrinth in a meadow. It was a rectangular piece of about 10 m width and 50 m length beside the football ground of a school. Within sight to the Schwanberg. First I wanted to make a circular labyrinth, because I had already some drafts for it. But then my look fell at the labyrinth cup  in the bookshelf with the Schwanberglabyrinth on it.

labyrinth cup

labyrinth cup

If that fitted on a cup, why not also in a rectangle? The center must not always be in the middle (from a circle). And thus I tried on a sheet of paper and soon had my draft. Not mathematically exact as I make this normally, but simply freehand.

draft

draft

The Schwanberglabyrinth is a Roman sector labyrinth (type Avenches) which is circled once. It is made of four meanders which are lined up. The passages can be devoured very smoothly into each other. One has this rhythm in the blood if one has dealt long enough with the labyrinth.

With the sheet of paper in the hand I marched before the lawn mower guided by a gardener of the city of Dettelbach, and thus this labyrinth came about. As a movement figure for the children in the break.

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The Seed Pattern in Labyrinths with Multiple Arms (continued)

In my last post I have shown that a seed pattern can also be drawn in labyrinths with multiple arms (see related posts). With the seed pattern for the Ariadne’s Thread it is possible to connect the arms in the shape of a flower (or a propeller). For each arm, a separate petal is needed.

Figure 1. Borderlines

Figure 1. Borderlines

These auxiliary figures can all be drawn in one continous  line.

Figure 2. How to Draw the Borderline

Figure 2. How to Draw the Borderline

Fig. 2 illustrates this with a three-arm labyrinth. Other flowers with multiple arms can be drawn the same way.

Each of the petals contains a part-seed pattern. I will show this using an example of one of my five-arm labyrinth designs. I choose the design KS 2-3 that has been installed as a temporary labyrinth on the square of Magdeburg cathedral. This labyrinth can be actually seen in the header of this blog. Otherwise there is an image of it here.

Figure 3. KS 2-3

Figure 3. KS 2-3

Fig. 3 shows the labyrinth in a drawing by Erwin of the walls and with the Ariadne’s Thread (red) inscribed.

Figure 4. Seed Pattern for the Ariadne's Thread

Figure 4. Seed Pattern for the Ariadne’s Thread

In fig. 4 the seed pattern for the Ariadne’s Thread is shown per se and completed to the whole Ariadne’s Thread. In order to complete this seed pattern, for each circuit 10 ends have to be connected with five segments of a circuit. Evidently, with an increasing number of arms, the seed pattern comes to look closer to the entire labyrinth. The part-circuits are shortened in relation to the part-seed patterns.

The seed pattern has first and most often been published for the walls of the Cretan type labyrinth. Also for several other one-arm labyrinths, seed patterns have been published. Therefore, the seed pattern does not constitute a characteristic attribute of the Cretan type labyrinth. It is not even a characteristic specific for one-arm labyrinths alone.

However, the use of seed patterns in labyrinths with multiple arms is of minor practical importance. The original purpose and meaning of the seed pattern was, that it enables us to capture the essential of a labyrinth with a simple memorable system of lines that allows us to generate the labyrinth straight away. And this applies best to the seed patterns of the Cretan type labyrinth and its relatives of the vertical line.

Figure 5. Seed Patterns of the Cretan Labyrinth and it's Relatives of the Vertical Line

Figure 5. Seed Patterns of the Cretan Labyrinth and it’s Relatives of the Vertical Line

Fig. 5 shows the seed patterns for the walls in the first column and for the Ariadne’s Thread in the second column. The corresponding types of labyrinths are on

  • row 1: Löwenstein 3
  • row 2: The Cretan
  • row 3: Hesselager
  • row 4: Tibble

 

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