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On my own behalf

Welcome to the Labyrinth

The topic of this blog is the labyrinth. Under nearly all aspects, I would like to arouse your interest on the fascinating lines and the meaning of this old object. Being an old surveyor I put my focus on the geometrical shape.
A new post should be published about twice a month. Meanwhile I am accompanied by Andreas Frei as coauthor.

Contents

In a blog the single posts (articles) are disposed in reverse order: the latest posts first, the older ones following. The display of the content is thus different from a website where it is always permanent.

Anyone who is looking for something special about labyrinths or just wants to know what he could find on this blog, maybe would like to have an overview.

I can provide this now and offer it as an own page titled Contents.

The register with the table of Contents is on top of the blog above the header image next to About us.

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For a better view

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In the last post I have presented four variants of the seed pattern of the Cakra Vyuh type labyrinth. Perhaps somebody might be interested, how the matching complete labyrinths look like. Here I will show them.

I thus add three other examples to the only example (Original) of this type of labyrinth that has been well known until now. Or, more exactly, only two of them are really new: the examples in the Classical and in the Concentric styles. I had already published the example in the Man-in-the-Maze style previously on this blog. Furthermore it has to be considered, that the original labyrinth rotates anti-clockwise. I have horizontally mirrored the three other examples. It is still the same labyrinth then, although rotating clockwise. I use to show all my labyrinth examples in clockwise rotation so they are more easily comparable.

Related Posts:

This is what a Baltic Wheel looks like:

The Baltic Wheel

The Baltic Wheel

It has circuits which run primarily about two turning points. The middle is empty, however, it has a second, short way to leave it directly. Thereby we also have two entries which are separated by a spoon-like formed part.
Historical examples are very rare. In Germany there is the Rad in der Eilenriede at the town park of Hannover. Otherwise we only know this type from literature.

In the previous articles I have dealt with the Wunderkreis. Besides, a certain resemblance between both these types has also struck me. Though both have two entries they are still different types. In what way are they different now?

The Wunderkreis

The Wunderkreis

The labyrinthine circuits are disposed around turning points which are arranged in a triangle. In the middle we have a double spiral (the circuits A, B, C) through which we leave the Wunderkreis. We have a walk-through labyrinth lying ahead of us.

The Baltic Wheel has a big, empty middle and consequently contains no double spiral. However, there is also the second access (or exit). If I leave out the circuits for the double spiral, I shall nearly get the  Baltic Wheel.

The intermediate stage

The intermediate stage

The remaining circuits are the same. Also the path sequence is the same. This shows the close relationship between the two labyrinth types.

Now I add a middle section formed from arcs between the two entrances and will thus receive a complete Baltic Wheel.

The Baltic Wheel

The Baltic Wheel

The Baltic Wheel can exist of a varied number of circuits. These can be added the same way as in the Wunderkreis (see related posts below).

Other design elements can also be added, such as an additional circuit around the whole Baltic Wheel.

Some years ago I had already published construction instructions for the Baltic Wheel. It looked a little bit different. The construction developed now seems easier to me and I like it better.

If I have fixed the number of the circuits for a Baltic Wheel, I can also begin with the base line of the triangle (between M3 and M4) and then determine the centre M1.

The construction has a dimension between axes of 1 m and therefore allows to scale it easier.

The drawing

The drawing

Here as a PDF file to look at, to print or to copy.

Related Posts

In the last post I have introduced the eleven-circuit Cakra Vyuh Labyrinth. Even though the seed pattern has a central cross and also can be easily drawn freehand, it is not a labyrinth in the Classical style. In fig. 1 I show the seed pattern in different variants.

CaVy_SP_var

Figure 1. Variants of the Seed Pattern

Image a shows the original seed pattern, image b the seed pattern in the Classical style, image c in the Concentric style, and image d in the Man-in-the-Maze style.

This figure clearly shows that the original seed pattern deviates from the Classical style. It is true that this seed pattern has a central cross as for instance the Cretan labyrinth also. However in the Cakra Vyuh seed pattern, from this cross further junctions branch off.

This is different in the Classical style. The Classical style consists of verticals, horizontals, ankles and dots. For this, no central cross is required. This page illustrates well, what I mean (left figure of each pair). If a seed pattern includes ankles these lie between the cross arms and do not branch off from them.

The four images in fig. 1 in part look quite different one from each other. So how do I come to the assertion that they are four variants of the same seed pattern? Let us remember that these figures show seed patterns for the walls delimiting the pathway. Now let us inscribe the seed patterns for the Ariadne’s Thread into these figures (fig. 2).

CaVy_SPab

Figure 2. With the Seed Pattern for the Ariadne’s Thread Inscribed

At first glance this looks even more complex. However, if we focus on the red figures, we will soon see what they have in common.

CaVy_SPa

Figure 3. Seed Pattern for the Ariadne’s Thread

The seed pattern represents a section of the entire labyrinth. More exactly, it is the section along the axis of the labyrinth. The turning points of the pathway align to the axis. This can be better seen on the seed pattern for the Ariadne’s Thread compared with the seed pattern for the walls delimiting the pathway.

In all four seed patterns, turns of the pathway with single arcs interchange with turns made-up of two nested arcs. This constitutes the manner and sequence of the turns and is the basic information contained in the seed pattern. In the four seed patterns shown, the alignment of the turns may vary from circular (image a, image d) to longisch, vertical, slim (image b, image c). The shape of the arcs is adapted to the shape of the walls delimiting the pathway. However in all images it is a single turn in alternation with two nested turns.

Related posts:

The previous post was more concerned with the geometry and the mathematically correct construction of the Wunderkreis in general.

Here is an example of how you can make it less theoretically. Denny Dyke from Circles in the Sand often creates double spirals and the Wunderkreis in his Dream Fields on the beach of Oregon. Denny Dyke has kindly shown me his method.
In the following photos it is explained.

Freehand he scratches the lines in the sand. Hence, the way runs between the lines. The double spiral has three arcs, the surrounding labyrinth has five circuits.

Step 1

Step 1

Denny begins with the lower part of the double spiral and draws three semicircles. On the left he adds two lines and the turning point, on the right there are three lines and the turning point (step 1).

Step 2

Step 2

Now he scratches three semicircles for the upper part of the double spiral. The first semicircle begins in the middle of the innermost lower semicircle (step 2).

Step 3

Step 3

All the other curves are drawn in parallel and equal distance to this arc by connecting all free ends of the existing lines and the turning points. Just the way we do it in the Classical labyrinth. We begin on top and draw four lines on the left side around the double spiral to the right side (step 3).

Step 4

Step 4

In the same way the two free lines below are connected together (step 4). Having done this the Wunderkreis has quite been completed.

The open lower middle section contains the two entries of the Wunderkreis. On the left side we enter the labyrinthine circuits. On the right side we have the exit out of the double spiral.

The completed Wunderkreis

The completed Wunderkreis

Denny has marked both accesses and has separated them through the “shoehorn” known from the Baltic wheel.

Related Posts

A Wunderkreis is a double spiral, surrounded by a simple labyrinth with two turning points.

We begin in the centre with the double spiral. One  semicircle below and one semicircle above the horizontal line would suffice as a minimum. Many more semicircles could be added to enlarge the double spiral. Here we make three arcs which we name A, B and C. The lower ones are drawn around M1 as the centre, the upper ones are arranged around M2 as the centre and shifted to the right.

Step 1

Step 1

Then we add three arcs on the left side. They are drawn in a triangular sector around the midpoint M1. We number the circuits from the outside with 1, 2 and 3. Circuit 3 will finally form the entrance.
The turning and midpoint M3 for the lower semicircle lies concentric between the both external circuits 1 and 2.

Step 2

Step 2

Now we go to the right side. Here two arcs more than on the left side are necessary, that means a total of five. Again we number the circuits from the outside inwards from 1 to 5. The circuit 5 will later lead to the exit.
The turning point M4 lies concentric between the four circuits 1 to 4. In the lower middle section two semicircles are traced around that midpoint M4.

Step 3

Step 3

Now the upper semicircles are completed around the midpoint M2. There are four semicircles (and circuits) more on each side than at the beginning.

Step 4

Step 4

The Wunderkreis is usually entered through the labyrinthine circuits on circuit 3 and left through the double spiral on circuit 5. The path sequence then is as follows: 3-2-1-4-C-B-A-A-B-C-5.
The path sequence 3-2-1-4 forms the basis of the meander, as connoisseurs know, as in the Knossos labyrinth.


Now we choose more circuits and apply the abovementioned principles to the construction. Through that Wunderkreise with a varied number of circuits can be generated. We can add circuits to the double spiral one by one, to the labyrinth we have to do it in pairs.
On the right side two circuits more are necessary than on the left. The lower turning points (M3 and M4) must lie concentric between the even-numbered left or right circuits. In the following example we have 6 circuits on the left and 8 on the right side.

If we know how many circuits for a Wunderkreis we want, we can lay both lower turning points on a line and determine the middle for the double spiral (M1) in a triangle. Entrance and exit can also be arranged  side by side without any space.

Nevertheless we can begin, while marking out, with the definition of the middle M1 and also determine the adjustment of the main axis (vertical line). The remaining centres M3 and M4 can afterwards be fixed in that triangle.

The main dimensions

The main dimensions

Best of all we consider the measurements as units, so either “metre” or “yard” or “step width” or something similar. Then we can also scale all dimensions.
The smallest radius begins with 1 unit and then gradually grows by 1 from arc to arc. Then the biggest radius has 12 units. The boundary lines add themselves on 407 units, the whole way through the Wunderkreis reaches 362 units.

The completed Wunderkreis

The completed Wunderkreis

In this example the Wunderkreis has four circuits more than in the other at the top of the page and no space between entrance and exit. This area is formed quite differently in the historical Wunderkreise. Sometimes the paths are joined together, sometimes they run apart.

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A very beautiful labyrinth example (fig. 1) named Cakra-vyuh can be found in Kern’s Book° (fig. 631, p. 294).

Andere 5

Figure 1: Cakra-Vyuh Labyrinth from an Indian Book of Rituals

The figure originates from a contemporary Indian book of rituals. In this, a custom of unknown age, still in practice today, was described, in which the idea of a labyrinth is used to magically facilitate birth-giving. To Kern this is a modified Cretan type labyrinth. I attribute it to a type of it’s own and name it after Kern’s denomination type Cakra-Vyuh (see Related Posts: Type or Style / 14).

The seed pattern is clearly recognizable. One can well figure out that this labyrinth was constructed based on the seed pattern. Despite this, I hesitate to attribute it to the Classical style. For this, the calligraphic looking design deviates too much from the traditional Classical style. The walls delimiting the pathway all lie to a mayor extent, i.e. with about 3/4 of their circumference on a grid of concentric circles. Therefore it has also elements of the concentric style. The labyrinth even somewhat reminds me of the Knidos style with its seamlessly fitting segments of arcs where the walls delimiting the path deviate from the circles and connect to the seed pattern.

Therefore I have not attributed this labyrinth to any one of the known styles, but grouped it to other labyrinths (Type or Style /9). However, I had also drawn this labyrinth type in the Man-in-the-Maze style already (How to Draw a Man-in-the-Maze Labyrinth / 5).

SPCV

Figure 2: Composition of the Seed Pattern

Fig. 2 shows how the seed pattern is made-up. We begin with a central cross. Tho the arms of this cross are then attached half circles (2nd image). Next, four similar half circles are fitted into the remaining spaces in between. Thus the seed pattern includes now 8 half circles (3rd image). Finally, a bullet point is placed into the center of each half circle. We now have a seed pattern with 24 ends, that all lie on a circle.

In the pattern it can be clearly seen, that the labyrinth has an own course of the pathway. Therefore, to me it is a type of it’s own.

Typ Cakra Vyuh

Figure 3: Pattern

Furthermore it is a self-dual, even though, according to Tony Phillips, uninteresting labyrinth (Un- / interesting Labyrinths). This because it is made-up of a very interesting labyrinth with 9 circuits with one additional, trivial circuit on both, the inside and the outside.

Related posts:

 

°Kern, Hermann. Through the Labyrinth – Designs and Meanings over 5000 Years. Munich: Prestel 2000.

What is a Wunderkreis?

It is only a labyrinth if we accept walk-through labyrinths as such, since it has two accesses and no middle in which one can remain. I also use the German term “Wunderkreis” and not the translated “wonder/miracle circle”.

I consider it as a real labyrinth and even state that it has older roots than the Cretan labyrinth from the Mediterranean area. The activity with the Babylonian labyrinths brought me to this view, as there is a double spiral in the centre of a typical Wunderkreis. But a spiral alone does not make a labyrinth, meandering patterns are also required.

Some examples:

Wunderkreis of stones

Wunderkreis of stones

This is a nice specimen laid with stones like the Scandinavian Troy Towns and probably also from this region. The way runs between the stones. The entrance lies in the middle below and then branches out. I can go on to the left or to the right. However, I must wander through the whole figure to come out again. In the centre the determining change of course takes place. The two turning points around which the way is led pendulously, lie on the left and on the right side. I move towards the middle or sometimes away of it; sometimes I turn right and sometimes I turn left, as I do in a classical labyrinth.
Two parts constitute the figure: the double spiral with the meander in the middle and the circuits around the two turning points. Which part will be run through first, depends on which way you choose. However, the two parts are not mixed, each element must be run for itself.

The element with the two turning points, which form a triangle in combination with the centre in the double spiral, also appears as own labyrinth type, such as the type Knossos, the Baltic wheel and the Indian labyrinth.

The Baltic wheel also has the second access/exit to the middle which  is very short, however. The real middle is formed by a bigger, empty area. Nevertheless, it is not a Wunderkreis, because the second way alone does not constitute one, but the double spiral in the middle.

Old drawing of the Eberswald Wunderkreis

Old drawing of the Eberswald Wunderkreis

In this drawing the paths rather than the walls are shown in black lines. The Wunderkreis was put on first in 1609 and to the quartercentenary in 2009 even a coin was designed.

Coin for the quartercentenary

Coin for the quartercentenary

Here the design looks a little bit different, nevertheless, the course of the path is the same as in the drawing. In the meantime, a Wunderkreis from paving-stones was put on again in Eberswalde. Not on the Hausberg like in 1609, but on the Schützenplatz.

The new Eberswald Wunderkreis

The new Eberswald Wunderkreis

Another historical Wunderkreis is passed down from Kaufbeuren.

Zeichnung des Wunderkreises aus Kaufbeuren

A similar Wunderkreis has been put on in 2002 in the Jordanpark again.

The 2002 restaured Kaufbeuren Wunderkreis

The 2002 restaured Kaufbeuren Wunderkreis

The Transylvanian Saxons brought new insights to the use of the Wunderkreis with the celebration of the march through it. The original Zeiden Wunderkreis still exists in today’s Romania. The Zeiden community have carried on the traditions round the Wunderkreis here in Germany so that we have learned more about that labyrinth.

Drawing of the Zeiden Wunderkreis

Drawing of the Zeiden Wunderkreis

The lines here illustrate the way and first turn to the right. They also do not branch out, but run apart. Thus we can assume that the external circuits were traversed first and then the double spiral.

At quite a different place the following temporary Wunderkreis was built in July 2015 : At low tide on the beaches of Bandon in Oregon (USA).

Dream Field at Face Rock on the beaches of Bandon

Dream Field at Face Rock on the beaches of Bandon, Photo © Courtesy of Pamela Hansen

Since 2014 Denny Dyke and his team have put on new creations under “Circles in the Sand” in the Dream Field Labyrinths. Besides, he often uses the double spiral and the Wunderkreis which is particularly suitable for these as it is a walk-through labyrinth. It does not depend on the external shape, a Wunderkreis can also be angular.


Now we can look at the most important features of the Wunderkreis in a sort of a blueprint. Here we have the limitation lines (walls) in black. We see four termini. The two entries are arranged side by side.

The walls of the Wunderkreis

The walls of the Wunderkreis

If we color the paths in different colours we can recognize better the essential components of this type of labyrinth. There are two different areas. If we enter through the left entrance we first surround the two turning points in the lower area in a pendular movement changing direction on every side. The way on the right leads into the double spiral.

The paths of the Wunderkreis

The paths of the Wunderkreis

The initial movement in a processional labyrinth first leads around the outermost circuits. In the double spiral the most important change of course takes place and leads out from there again.
The Wunderkreis was often used for competitions and even served as a sort of racetrack. Maybe the name can be traced back to this use as well.

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