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We take a 7-circuit classical labyrinth and number the single circuits from the outside inwards. “0” stands for the outside, “8” denotes the center. I take this two numbers into the circuit sequence, although they are no circuits. As start and end point they help to better understand the structure of the labyrinth.

Ariadne's thread in the 7-circuit labyrinth

Ariadne’s thread in the 7-circuit labyrinth

The circuit sequence is: 0-3-2-1-4-7-6-5-8

Everybody which already has “trampled” Ariadne’s thread (the path) in the snow knows this: Suddenly there is no more place in the middle, and one simply goes out. And already one has created a walk-through labyrinth. This is possible in nearly all labyrinths.

Then maybe it looks like this:

Ariadne's thread in a walk-through labyrinth

Ariadne’s thread in a walk-through labyrinth

If one wants a more compact labyrinth, one must change the shape. The internal circuits become, in the end, a double spiral. We can make either two separate ways or join them. So we will get a bifurcation.

Just about:

The 7-circuit walk-through labyrinth

The 7-circuit walk-through labyrinth

We will get the following circuit sequence if we take the left way or the fork to the left:
0-3-2-1-4-7-6-5-0

Now we take first the right way or the fork to the right, then the circuit sequence will be:
0-5-6-7-4-1-2-3-0

Because the two rows are written among each other, they simply can be add up together (without the first and the last digit):
8-8-8-8-8-8-8

This means: If I go to the left, I am in the original labyrinth, if I go to the right, I cross the complementary one.

The complementary labyrinth of the 7-circuit labyrinth

The complementary labyrinth of the 7-circuit labyrinth

It has the circuit sequence 0-5-6-7-4-1-2-3-8.

Or said in other terms: The walk-through labyrinth contains two different labyrinths, the original one and the complementary one.

The 7-circuit labyrinth is self-dual. Therefore I only get two different labyrinths through rotation and mirroring as Andreas has described in detail in his preceding posts.

How does the walk-through labyrinth look if I choose a non self-dual labyrinth?

I take this 9-circuit labyrinth as an example:

A 9-circuit labyrinth

A 9-circuit labyrinth

Here the boundary lines are shown.
On the top left we see the original labyrinth, on the right side is the dual to it.
On the bottom left we see the complementary to the original (on top), on the right side is the dual to it.
However, this dual one is also the complementary to the dual on top.

The first 9-circuit walk-through labyrinth

The first 9-circuit walk-through labyrinth

The first walk-through labyrinth shows the same way as in the original labyrinth if I go to the left. If I go to the right, surprisingly the way is the same as in the complementary labyrinth of the dual one.

And the second one?

The second 9-circuit walk-through labyrinth

The second 9-circuit walk-through labyrinth

The left way corresponds to the dual labyrinth of the original. The right way, however, to the complementary labyrinth of the original.

Now we look again at a self-dual labyrinth, an 11-circuit labyrinth which was developed from the enlarged seed pattern.

An 11-circuit labyrinth in Knidos style

An 11-circuit labyrinth in Knidos style

The left one is the original labyrinth with the circuit sequence:
0-5-2-3-4-1-6-11-8-9-10-7-12

The right one shows the complementary one with the circuit sequence:
0-7-10-9-8-11-6-1-4-3-2-5-12

The test by addition (without the first and the last digit):
12-12-12-12-12-12-12-12-12-12-12

Once more we construct the matching walk-through labyrinth:

The 11-circuit walk-through labyrinth

The 11-circuit walk-through labyrinth

Again we see the original and the complementary labyrinth combined in one figure. If we read the sequences of circuits forwards and backwards we also see that both labyrinths are mirror-symmetric. This also applies to the previous walk-through labyrinths.

Now this are of all labyrinth-theoretical considerations. However, has there been such a labyrinth already as a historical labyrinth? By now I never met a 7- or 9-circuit labyrinth, but already an 11-circuit walk-through labyrinth when I explored the Babylons on the Solovetsky Islands (see related posts below). Besides, I have also considered how these labyrinths have probably originated. Certainly not from the precalled theoretical considerations, but rather from a “mutation” of the 11-circuit Troy Towns in the Scandinavian countrys. And connected through that with another view of the labyrinth in this culture.

There is an especially beautiful specimen of a 15-circuit Troy Town under a lighthouse on the Swedish island Rödkallen in the Gulf of Bothnia.

A 15-circuit Troy Town on the island Rödkallen

A 15-circuit Troy Town on the island Rödkallen, photo courtesy of Swedish Lapland.com, © Göran Wallin

It has an open middle and the bifurcation for the choice of the way. This article by Göran Wallin on the website Swedish Lapland.com reports more on Swedish labyrinths.

For me quite a special quality appears in these labyrinths, even if there is joined a change of paradigm.

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According to Wikipedia there are in all about 35 labyrinths in the Solovetsky Islands in the Onega Bay of the White Sea in the  Arkhangelsk Oblast (Russia), about 500 km to the north of St. Petersburg and 150 km to the south of the polar circle.

The Labyrinth on the Bolshoy Solovetsky Island

The Labyrinth on the Bolshoy Solovetsky Island, Source: Wikipedia, Photo © Vitold Muratov 2013

How old are they, who has built them, what was the purpose? There are many speculations about that (see the Further Links below). I do not want to take part in it.
I only want to find out how they look like, which type of labyrinth they are. I have found enough indications. There are several photos which reveal a part of the labyrinths quite well, unfortunately, not completely.

On the Internet I have found the following graphics from a book published in 1927 by Nikolai Vinogradov (historian, ethnologist and folklorist, 1876 – 1938).

Graphics of a stone setting

Graphics of a stone setting

In Hermann Kern’s book “Labyrinths” I have found the photo of a petroglyph on the island Skarv in the Stockholm archipelago (Sweden), presumably from the 18th/19th century.

Petroglyph on the Skarv Island

Petroglyph on the Skarv Island, Source: Hermann Kern, Labyrinthe, 1982, fig. 583 (German edition); Photo: Bo Stiernström, 1976

Compared to the graphics above the labyrinth is mirrored and the double spiral has a circuit less.

The labyrinths, called Babylons in the local dialect, have been made in the same way as the Scandinavian Troy Towns, probably at the same time and presumably served similar purposes.
Nevertheless, the layout is completely different. There are none of the well-known 11- or 15-circuit Cretan labyrinths which can be made from the enlarged seed pattern.

They belong to the walk-through labyrinths. These have a double spiral in the middle and labyrinthine circuits round two turning points. They can have two accesses or only one, however, with a bifurcation.

The hints, the Babylons could be seen as part of a cult of the dead and would show two snakes winding into each other, well explain the figure. They could also have been put on as a sort of piece of art.

There appear two spirals interlocking into each other. In a geometrical figure with semicircles around different centres they can be constructed as follows:

Blue and red spirals

Blue and red spirals

Both lines can be drawn well in one go and freehand: You will begin in the middle, turn to the right, circling once around, then in a larger turn outwardly from the right side to the left, from there inwards back to the right side. The red line ends her, the blue returns one more time to the left, circling inwards.
When you know how to draw each line, try to draw one in the other. Best begin with the blue line and leave enough space between the lines. Then put the red line in between.
That sounds complex, and it is. But best of all try several times with a pencil on a sheet of paper.

The result should look like thus:

The red spiral inside the blue one

The red spiral inside the blue one

For a labyrinth laid of stones these semicircular or elliptical curves can relatively simple be realised.

Best of all one starts in the middle. There one can arrange most easily the thickening of the ends and the interpieces. Then the remaining lines follow in steady distances.

Step 1 and 2

Step 1 and 2

One makes three semicircles downwards (step 1), and four semicircles upwards (step 2). Thus the double spiral in the middle is built.

Step 3 and 4

Step 3 and 4

Then I add five semicircles on top (step 3). There are five free ends on the left side, and seven on the right. These I elongate to the sloped line at right and at left (step 4).

Step 5 and 6

Step 5 and 6

In step 5 I connect both outermost free ends on the left and on the right side so with each other that in the middle a gap remains for the entrance. In step 6 the remaining free ends are connected parallel to the curves just made before. The innermost free end on each side will be the turning point.

It is noteworthy that the limitation lines do not overlap like they doe in the Cretan labyrinth. In spite of the bifurcation the way through the whole figure is unequivocal and follows the typical “labyrinthine” rhythm.

The construction elements

The construction elements

Even if the Babylons were not put on so geometrically precisely, nevertheless, these geometrical features show the essential internal structure and let them count to the Wunderkreise. I would like to call them Babylonian Wunderkreise to discern them from the Wunderkreise with two accesses side by side like we see that in the Zeidner Wunderkreis.

The Babylons are related to the Babylonian Labyrinths through the double spiral in the middle and the unequivocal way that leads to it, even if there are two opposite entrances.

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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. 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 Eberswalde Wunderkreis

Old drawing of the Eberswalde 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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or, freely adapted from a song by Herbert Grönemeyer (German musician):

When is a Labyrinth a Labyrinth?

My researches on Wikipedia about the labyrinth have inspired me once again to try an own definition of the labyrinth. This is my proposal:

The labyrinth is (at first sight) a confusing, nevertheless unique, purposeful, artful and meaningful system of lines. The labyrinth, strictly spoken, leads (as a rule) on an unbranched, winding path to the aim, mostly in the middle. The labyrinth, broadly defined, has a branched system of lines with more options, dead ends and loops and is called a maze. The labyrinth as a metaphor signifies confusing and mostly difficult facts and circumstances.

Classical 7-circuit labyrinth with a larger centre

Knidos Labyrinth

Ariadne's Thread (path) in a classical 7-circuit labyrinth

Ariadne’s Thread

Hedge Maze Schönbusch (Germany)

Maze

Classical 3-circuit labyrinth

Simple Labyrinth

Classical labyrinth with 4 circuits and an additional path

Type Baltic Wheel

Type Gossembrot with 5 axes and 7 circuits

Type Gossembrot

Schwanberg Labyrinth (4 divisions)

Type Schwanberg

Calligraphic Labyrinth by Ingeborg E. Müller

Calligraphic Labyrinth

Crossing Labyrinth by Alana Forest

Crossing Labyrinth

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This is probably too long, sounds to complex and looks, hence, quite labyrinthine. Maybe the first sentence would be enough, because it does not exclude the maze and admits the exceptions.

A labyrinth is not always unbranched and totally without every option. Otherwise, the type Baltic wheel (such as the Rad in der Eilenriede at Hannover) would not be a labyrinth. The aim also is not always the middle, especially the geometrical middle or the centre. The Wunderkreis of Kaufbeuren with branching paths is without a real middle and is rather a passageway labyrinth, hence, very well suitable for pageants.

Also the change of course in the movement belongs not necessarily to the labyrinth, because, otherwise, a 3 circuit labyrinth or some modern forms would not be a labyrinth. One can even accept crossroads, like in the Crossing labyrinth of Alana Forest from Australia, because the alignment is unequivocal. One may neither turn left nor right, but always go straight ahead.

Labyrinths and mazes have a lot in common and are related. In colloquial English, labyrinth is generally synonymous with maze. A maze is also a labyrinth (in the broader sense), but a labyrinth (strictly spoken) is not a maze. Since one cannot get lost in it. But it can be bewildering and irritating (at first sight).
I believe, the confusion also comes along that we speak of the labyrinth in the strict sense from a single path free of crossroads and branches and then we show the boundary lines of the labyrinth. Besides, the information refers to the path, Ariadne’s thread, which lies between the boundary lines and is not visible in this form of expression. Just this happened to me at the beginning of my acquaintance with the labyrinth. Only the second and more exact look makes clear the right correlations.

It is the fascination of the labyrinth that it is an ancient, archaic human symbol to be found in different cultures, religions and time epochs and that is open for many interpretations and approaches. This is why it is also qualified for our current time and world as a universal symbol. However, nobody should claim for himself the interpretational sovereignty.

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or:

How could the Troy Towns in the Scandinavian countries have been built ?

The oldest and most of walkable labyrinths throughout the world are found there. And nearly all are made of field stones in all sizes. So it can be assumed that the homeland of the labyrinths lies there.

In the meantime we know how to draw a classical 7-circuit labyrinth. Building one can be proceeded in the same way. One puts the basic pattern, that is arranged in a square, and goes on in curves. Instead of using stones one can make it with sawdust or bark mulch or logs or any other objects.

The best way is to begin inside and then going outwards. You can do it alone or together with others. Then you must agree on what to do and how to connect the lines.

If you want to make a permanent labyrinth, you should think about the overall size, the width of the path, the alignment and the exact position.

The example shown here is a labyrinth with 11 circuits, thus 4 more than usual. The 4 more results simply from the fact that in the 4 quadrants of the square still one further angle is inserted.
And you may guess it: Adding still 4 angles more results in a labyrinth with 15 circuits, and so on.

Thus the Swedish Troy Towns, that I could explore last year, could have been developed.

The seed pattern

The seed pattern

The first arch (=the center)

The first arch (=the center)

Four arches

Four arches

Five arches

Five arches

Nine arches

Nine arches

Ten arches

Ten arches

Eleven arches

Eleven arches

Twelve arches (=11 circuits)

Twelve arches (=11 circuits)

One must simply connect the last free stone on the one side (left of the center) with the last free stone on the other side (right of the center) in a curve parallel to the preceding one.

Here a small 7-paths labyrinth, put 2007 at the beach of Folhammar (Gotland, Sweden) by Lisa.

Stone labyrinth (8 walls, 7 circuits)

Stone labyrinth (8 walls, 7 circuits)

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A year ago I have reported about the Swedish Troy Towns on mymaze and there also about the special design of a labyrinth in bypass mode.
You see, there are labyrinths for nearly all purposes. We still had a Heart Labyrinth.

How does the bypass look like?
Here the pattern from the book Gotländskt Arkiv 1983, in which John Kraft writes about the Swedish Troy Towns. The sketch is of Bo Stjernström, a further Swedish labyrinth specialist.

The Seed Pattern

The Seed Pattern

You see the probably well-known basic pattern with the variant to produce a bypass.

Here a design of the complete labyrinth, so that one can reconstruct the entire alignment.

Bypass Labyrinth with 10 Circuits

Bypass Labyrinth with 10 Circuits

Without the bypass that would result in a labyrinth with 11 circuits, so we have only 10 circuits.

And here Ariadne’s thread:

Ariadne's Thread

Ariadne's Thread

Now don’t ask me for which such a labyrinth was good.
Perhaps one for heart patients? Because one has to walk less? Because one goes nearer to the center? Because the center is larger? Because less is sometimes more?

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is the (translated) title of a book by Dr. Ernst Krause from the year 1893.
And because the complete title contains (nearly) the complete book, here the title page is shown:
Attention: This is all in German and the characters are old German too.

The title of the book

The title of the book

The book says essentially that all the legends concerning the Troy Towns are of Nordic origin. The original labyrinths are the Troy Towns, above all the oldest that can be walked. There are still about 300 of this old Troy Towns in Scandinavia. For me the homeland of the labyrinth is there.
If one speaks from the labyrinth, most are thinking at first of the maze with its complicated, devoured, unclear ways, which leads only, if at all, after many running and erring, into the center.
For “advanced learners” it is clear that in a labyrinth there is only one and a clear way to the center. And that this way inside is also the way outside.
Many others connect the labyrinth with the Greek mythology, where is spoken of King Minos, the hero Theseus, the king’s daughter Ariadne, the monster Minotaur, the architect Daedalus and their acts.

Ernst Krause tried to prove that the whole labyrinth idea is to be settled rather in the Nordic culture. His ideas are sometimes difficult to understand, above all if one is not so familiar with the many aforementioned shapes and events.
Thus we know in the long run still too few about the origin and the meaning of the labyrinth.
His theory, how the labyrinth could have developed from the circle figure, is today no longer recognized.
He was very pleased, when during or after the writing of his book the famous jug of Tragliatella was found, which underlines his ideas. Thus he wrote directly still another supplement to his book, which is attached as appendix in my second-hand acquired exemplar.

The appendix

The appendix

What remains after all that?

  • That it is probably not so important to know exactly where the labyrinth comes from, who invented it, or whether it was independently developed at different places. We can see the labyrinth however in larger and further connections, than so far assumed.
  • That the labyrinth can be still fascinating and it depends on us what we make out of it.

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