Feeds:
Posts
Comments

Posts Tagged ‘Wunderkreis’

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

Read Full Post »

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

Read Full Post »

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.

Related Posts

Read Full Post »

And vice versa: How to make a Wunderkreis from a Babylonian visceral labyrinth.

That’s possible, at least with the Babylonian Umma Labyrinth.

The essentials of a labyrinth ly in the course of the pathway expressed by the level sequence, not the external form or layout. More exactly Andreas calls this the pattern.

The Babylonian Umma Labyrinth

The Babylonian Umma Labyrinth

The Umma labyrinth has two turning points surrounded by two circuits each and a meander in the middle. The two entries ly outside. There is only one, unequivocal way through the labyrinth.

The Wunderkreis has a double spiral in the centre and two other turning points with arbitrarily many circuits. Besides, a side has a circuit more than the other. The entries are in the middle section.

A large Wunderkreis

A large Wunderkreis

In order to indicate the single developing steps I first transform a “completely developed” Wunderkreis into the smallest possible version.

It looks thus: A meander in the middle and two other turning points with a total of three circuits as to be seen in the labyrinth type Knossos.

The smallest Wunderkreis

The smallest Wunderkreis

To be able to compare this small Wunderkreis to the Umma labyrinth, I lay all centres (at the same time the ends of the boundary lines or the turning points) on a single line. Just as if I folded the triangle built from the turning points.

The compressed Wunderkreis

The compressed Wunderkreis

Both entries are here in the middle section, in the Umma labyrinth they are outside and side by side. Besides, there is one more circuit on the left side. Now I add one circuit to the figure and the entry will change to the outer side on the right as well.

One more circuit

One more circuit

I now turn the second entry to the left side. As a result, the two entries  point in different directions.

The two entries outside

The two entries outside

Hence, I turn the right entry completely to the outer side on the left beside the left entry. As I do that geometrically correct, two empty areas appear.

The two entries side by side

The two entries side by side

Now I extend both entry paths by a quarter rotation upwards and turn the whole figure to the right by some degrees . Thus I receive the complete Umma labyrinth.

The Babylonian Umma Labyrinth

The Babylonian Umma Labyrinth

If I want to develop the Wunderkreis from the Umma labyrinth, I must leave out some circuits, turn the whole figure and finally raise the middle part.

The nucleus

The nucleus

The supplements made in the preceding steps are emphasised in colour. The nucleus of the visceral labyrinth contains the Wunderkreis.

Surely the Wunderkreis as we know it nowadays was not developed in this way. There are no historical documents to prove that. However, in my opinion the relationship of both labyrinth figures can be proved thereby. They are not simply spirals or meanders. These elements are rather included and connected in a “labyrinthine” way.

Related Post

Read Full Post »

At the 22nd Zeiden neighborhood get-together on June 6th 2015 in Dinkelsbühl marching through the Wunderkreis was one of the highlights.

In my first post from June 21st 2015 I wrote extensively about the Wunderkreis itself and the more “technical” aspects (see Related Post below).

For those who want to know something more about the historical background, I recommend reading the article by Richard Myers Shelton in Caerdroia 44 or to get informed by the articles mentioned in Related Links. The people of Zeiden themselves have written about their traditions and their customs.

In this post, it’s more about the march through the Wunderkreis itself.

Set on a beautiful day in a beautiful environment, i.e. in the heart of the well-preserved medieval Dinkelsbühl, this event was one of the highlights at the 22nd Zeiden neighborhood get-together on the old pavement in front of the “Schranne”.

The temporary Zeiden Wunderkreis in Dinkelsbühl

The temporary Zeiden Wunderkreis in Dinkelsbühl

The through traffic was blocked off the Weinmarkt this afternoon and so many astonished tourists were marvelling at the white lines on the pavement.
A local baker (picture 7) baked about 250 Kipfel specially for this day. The march itself took about 15 minutes. After that the Zeiden brass band offered another open-air concert, where some brave couple even danced.

On this day I had the opportunity to meet the current neighbor father Rainer Lehni (pictures 8, 11) and the old neighbor father  Udo Buhn (Figure 20), and spoke with the people of Zeiden themselves.

Photogallery:

Clicking on a picture will open the carousel, clicking × in the top left-hand corner of the carousel, or the “Esc”- key on your keyboard,  will close it.

Numerous participants walked along the lines of the Wunderkreis to the sound of the traditional Kipfelmarsch, performed by the Zeiden brass band and were each rewarded with a Kipfel (croissant).

Probably we will now have to wait some more years until the next march through the Wunderkreis?

Although the original Zeiden Wunderkreis still exists in today’s Codlea (now Romania), it would be fine if the Zeiden Transylvanian Saxons could continue their tradition here in their new homeland of Germany with a new permanent Wunderkreis.

Note for TLS members: Read the excellent article by Richard Myers Shelton in Caerdroia 44 (April 2015) about the Transylvanian Wunderkreis.

Related Post

Further Links (Sorry, in German only)

The Zeiden Wunderkreis

The Zeiden Wunderkreis

Read Full Post »

At the 22nd Zeiden neighborhood get-together in Dinkelsbühl (Bavaria, Germany) I could be present when the ambitious Zeiden helpers outlined the temporary Wunderkreis (translated literally wonder circle) on 6th June 2015.

Most of the Transylvanian Saxons in today’s Germany came from Transylvania (now Romania) originally and have a special connection to Dinkelsbühl through the association of the Transylvanian Saxons.

It is astonishing how long the tradition of marching through the Wunderkreis to the sounds of the historical Kipfelmarsch has been preserved.
For more information go to Further Links on the bottom of this page.

As a trained surveyor and “Labyrinthologist” I was mostly interested in how the knowledge of building the Wunderkreis has been passed on from one generation to the next. I could see the sketch and at the same time watch how they did it.

Zeiden Wunderkreis

Zeiden Wunderkreis, reconstructed using a sketch by the late Thomas Dück

Here the freehand sketch by Rainer Lehni for the work in situ:

Freehand sketch by Rainer Lehni

Freehand sketch by Rainer Lehni

At the first glance it looks unspectacular seeing only lines, some figures and few measurements. The lines show the way in the labyrinth, the so-called thread of Ariadne, which all walkers will follow. Therefore the lines do not represent the boundary lines, as they usually do in other labyrinths.

The internal structure of a labyrinth is the most important property which is displayed in the path sequence for example. In this case we can find a double spiral and a meander, based on a triangle. The two accesses to the labyrinth, named as start and end in the drawings, are a specific feature. In the middle the direction changes, therefore we speak of a pass-through labyrinth.

In the following pictures we watch the “supporting workers” of the Wunderkreis doing their job.

Clicking on a picture will open the carousel, clicking × in the top left-hand corner of the carousel, or the “Esc”- key on your keyboard,  will close it.

Being a trained surveyor I was able to convert this into a drawing (see below).

The Zeiden crew chose 60 cm as a basic measure, this is the distance from line to line, being the path width at the same time. All further measures result from there. The smallest semicircle has a radius of 30 cm; in distance of 60 cm the additional elements follow. The biggest diameter (the belly extent) in the outermost circuit (named 1 in the drawing) amounts to 13.80 m. The length of the whole way through the Wunderkreis amounts to ca. 236 m.

The level of efficiency (detour factor) is 37 or even 40, if one begins at the end.

The whole labyrinth is composed of curve sections which are determined from four central points (M1 – M4), joined together without sharp bends. The order while marking out the curve sections could be any. Nevertheless, it is more useful to begin with the upper semicircles (in Green) around M4. Afterwards the curves around M3 (brown) and in the end those around M2 and M1 will follow.

The main construction points (M1 – M3) form a triangle. M4 is added to the left. One should mark out these points before drawing the curve elements. Thereby one gains a better overview of the location of the Wunderkreis on site.
The “base line” between M1 and M2 could be narrowed down a little.

While walking the Wunderkreis, at first the five external circuits (1 – 5) are wandered through. These correspond to a simple labyrinth. The following seven circuits (6 – 12), built by closely intertwined spiraling curves, correspond to a double spiral with the change of direction in the middle of a meander.

The entry into the labyrinth takes place to the right in the 5th circuit, the exit in the 7th circuit.

When the marchers come out of the exit they will be rewarded with a Kipfel (croissant), a unique custom worldwide .

The layout drawing

The layout drawing

The following photos show the the main construction lines in blue, the situation of the central points in red, and the numbering of the circuits from the outside inwards from 1 to 12. Through that we can get the so-called path sequence, the order in that the circuits strode through, such as start-5-2-3-4-1-6-8-10-12-11-9-7-end. This is so to speak the internal structure of the Wunderkreis, virtually the rhythm.

Lines on the cobbles of Dinkelsbühl

Lines on the cobbles of Dinkelsbühl

The construction lines (in Blue) and the midpoints (in Red)

The construction lines (in Blue) and the midpoints (in Red)

The numbering of the lines from the outside inwards

The numbering of the lines from the outside inwards

Ready to go

Ready to go

So, and now we are ready to go. The following photos show that the march through the Wunderkreis may be confusing at first sight.

A little tip: Follow the red point in the pictures 1 – 16 on the way through the Wunderkreis, because it marks the leader.

Clicking on a picture will open the carousel, clicking × in the top left-hand corner of the carousel, or the “Esc”- key on your keyboard,  will close it.

In the history of the labyrinth the miracle circles (even called “Wunderkreis” in English) represent a unique form of the labyrinth which existed and still exists in Germany and the Baltic countries.

We know some Wunderkreise from the literature.
Among the four historical remaining labyrinths in Germany we count the Wheel in the Eilenriede in Hannover (originally from 1642), and the Kaufbeuren Wunderkreis (originally from 1846), rebuilt after historical documents in 2002 in the Jordanpark of Kaufbeuren (read more in Caerdroia 34).

The first Wunderkreis of Eberswalde from 1609 was honoured in 2009 to the 400-year-old jubilee with a loyalty thaler and the third Wunderkreis was rebuilt in 2013 after historical documents on the Hausberg.

Although the Zeiden original Wunderkreis exists still in today’s Codlea (now Romania), it would be fine if the Zeiden Transylvanian Saxons could continue their tradition here in their new homeland Germany with a new permanent Wunderkreis.

This would be a wonderful contribution to the cultural history of the labyrinth with this unique Zeiden Wunderkreis and its special characteristics.

… To be continued

Hint for TLS members: Read the excellent article from Richard Myers Shelton in Caerdroia 44 (April 2015) about the Transylvanian Wunderkreis.

Related Post

Further Links (Sorry, in German only)

The Zeiden Wunderkreis

The Zeiden Wunderkreis

Read Full Post »

I have already written about the Babylonian visceral divination labyrinths and tried to prove their relationship with the labyrinth. They date to the Middle Babylonian and Neo-Babylonian time (ca. 1500 to 500 BC).

However, there are even older labyrinth representations from Old Babylonian time (ca. 2000  to 1700 BC) which look quite differently than the visceral labyrinths and which can probably be taken for the ancestors of the labyrinth.

The Swedish historian of Babylonian mathematics and cuneiform script expert Jöran Friberg has studied the Babylonian mathematical  tablets of the Norwegian Schøyen Collection in detail and has documented that in 2007. He calls the following figures labyrinths and tries to prove that.

In the journal Caerdroia 42 Richard Myers Shelton has written extensively on the subject of the Babylonian Labyrinths. Most of my information I got from him. Here it is a matter for me of founding in what the relationship with the labyrinth consists.

One must take therefore the following representations as the oldest labyrinths known so far.

Here a rectangular labyrinth labelled MS 3194 in the Schøyen Collection:

The rectangular labyrinth MS 3194

The rectangular labyrinth MS 3194, source: Schøyen Collection

We do not know anything about the purpose of this figure. It could have served quite philosophical or mathematical considerations.

In what does the relationship with the labyrinth exist now?

We must look at it more exactly. Richard Myers Shelton could reconstruct the lines on the clay tablet perfectly and therefore I can present a colored drawing of the entire figure.

The rectangular Babylonian labyrinth

The rectangular Babylonian labyrinth

The thin black lines limit the ways. These are the free space between the lines. There are two open entries to the rectangle. One entrance lies roughly in the middle of the left side, the other one opposite on the right. The way from the left is highlighted in ochre, from the right in green. In the middle they meet and change the direction. The one way is leading in, so to speak, and the other out.

There are no forks or dead ends. The whole, long and winding path must be accomplished. The entire rectangle is crossed.

The layout shows a certain, but not quite successful symmetry. The last laps round the center remind a double spiral. The other circuits are intertwined in the shape of meanders.

We have thus an unambiguous, doubtless and purposeful way through a closed figure, as we know it from a “true” labyrinth.

Then there is still a square labyrinth labelled MS 4515. Here the colored drawing:

The square Babylonian labyrinth

The square Babylonian labyrinth

Maybe it should represent a town? As we know that from other labyrinths. With gates, bastions, walls?


Amongst the Babylonian tablets is another one with geometrical illustrations. Jöran Friberg calls them mazes. They are quite sure not.

One could consider these lines as labyrinthine finger exercises. Some are difficulty to reconstruct. So, Friberg and Shelton come to different results.

There are two rows with four fields in which a rotationally symmetric closed path runs without beginning and end through four sectors. All areas are mostly touched, sometimes there are inaccessible places. One is reminded of the Roman sector labyrinths many centuries later.

The tablet MS 4516

The tablet MS 4516, source: Schøyen Collection

Here the drawings of two fields:
The first field on top left

The first field on top left

The fourth field on bottom left (reconstructed)

The fourth field on bottom left (reconstructed)

Clearly one recognises the meander, the symmetrical arrangement and the alignment of the paths between the black lines.

Much later similar representations on the silver coins of Knossos are found:

Swastika meander

Swastika meander on a coin, 431-350 BC / source: Hermann Kern, Labyrinthe, 1982, fig. 49 (German edition)

The right “ingredients” for a labyrinth, namely meander and spiral were already known in Old Babylonian times. The idea of a confusing, winding, nevertheless unequivocal way in a restricted space with rhythmical movement changes can have originated from there.

We can push back the time for the origin of the labyrinth some hundred years later to the time about 1800 BC. At first it was the idea of a walk through labyrinth. The further development happened in Middle to New-Babylonian times in the intestinal labyrinths with also two entries, yet unambiguous way.

Since 1200 BC we know the Cretan labyrinth with only one entry and the end of the path in the center. We could call this a way in labyrinth whereas the Babylonian labyrinth is a way through labyrinth.

Till this day have remained walk through labyrinths in the type of the  Baltic wheel and the Wunderkreis (wonder circle). We recognise them as real labyrinths, although they also have two entrances and do not end in the middle.

The Kaufbeuren Wunderkreis

The Kaufbeuren Wunderkreis

More information is to find about the Babylonian labyrinths in an excellent article by Richard Myers Shelton in Jeff Sawards Caerdroia 42 (March 2014), and in a new article from him in Caerdroia 44 (April 2015) about the Transylvanian Wunderkreis.

Related Posts

Further Links

Read Full Post »

« Newer Posts - Older Posts »

%d bloggers like this: