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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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I have written quite in detail about the Babylonian labyrinths. For that I refer to the Related Posts below. Now here it should be a summary.

I have taken most information from the detailed and excellent article of Richard Myers Shelton in Jeff Sawards Caerdroia 42 (March 2014) to which I would also like to point here once again.

The findings are in the most different collections and museums worldwide. I use the catalogue number to describe the various clay tablets.

The oldest specimens in angular shape dates back to Old Babylonian times about 2000 – 1700 BC and are to find in the Norwegian Schøyen Collection.

The Rectangular Babylonian Labyrinth MS 3194

The Rectangular Babylonian Labyrinth MS 3194

The Square Babylonian Labyrinth MS 4515

The Square Babylonian Labyrinth MS 4515

Then follows the different more round visceral labyrinths from the Middle Babylonian to the Neo-Babylonian times about 1500 – 500 BC. They are to be found in the Vorderasiatisches Museum Berlin (VAN… and VAT… numbers), in the Louvre (AO 6033), in the Rijksmuseum van Oudheden Leiden (Leiden labyrinth) or come from Tell Barri in Syria (E 3384).

I have numbered the tablets with more figures from the left on top to the right below and present the well visible ones (21 pieces) in a bigger tracing. Some figures are unrecognisable or destroyed. All together we have 48 illustrations.

Then there are another 6 single specimens. They follow here:

Visceral Labyrinths

Visceral Labyrinths

Here the 21 bigger tracings of the well recognisable specimens:

The Visceral Labyrinth on VAT 984

The Visceral Labyrinth on VAT 984

The Visceral Labyrinths on VAN 9447

The Visceral Labyrinths on VAN 9447

The Visceral Labyrinths on E 3384 recto

The Visceral Labyrinths on E 3384 recto

The Visceral Labyrinths on E 3384 verso

The Visceral Labyrinths on E 3384 verso

So we have a total of 56 Babylonian labyrinths, 29 of which are clearly recognisable.

It is common to all 29 diagrams that they show an unequivocal way which is completely to cover. There are no forks or dead ends like it would be in a real maze.

All 29 specimens have a different layout or ground plan and therefore no common pattern.

Everyone (except VAT 9560_4) has two entrances. On the angular labyrinths they are lying in the middle of the opposite sides. On the remaining, mostly rounded specimens they are situated side by side or are displaced.

The Leiden Labyrinth is simply a double spiral. An other special feature is the visceral labyrinth VAT 9560_4. It has only one entrance and a spiral-shaped centre, just as we have that in the Indian labyrinth. It shows perfectly a labyrinth.

The Mesopotamian divination labyrinth could also have a closed middle (and therefore only one entrance) and the loops run in simple serpentines.

The remaining 24 specimens have all a much more complicated alignment with intertwined bends and loops.

The 27 unreadable specimens are presumably structured alike. And maybe there are still more clay tablets awaiting discovery?

We know nothing about the meaning of the angular specimens. The remaining 27 more rounded specimens are visceral labyrinths.

The visceral labyrinths show the intestines of sacrificial animals as a pattern for diviners, describing how to interprete them for oracular purposes in the extispicy. From there it is also to be understood that they should look very different. This explains her big variety. And also again her resemblance. They represent rather an own style than an own type.

The Babylonian labyrinths come from an own time period, from another cultural sphere and follow a different paradigm than the usual Western notion of the labyrinth. They are above all walk-through labyrinths. However, in our tradition we also know walk-through labyrinths, especially the Wunderkreis.

A Wunderkreis in Babylonian style

A Wunderkreis in Babylonian style: The logo for the gathering of the Labyrinth Society TLS in 2017), design and © Lisa Moriarty

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The Wunderkreis and the Baltic Wheel are compound labyrinths which are constructed from curves around different centres. The two lower turning points are proper for the “labyrinthine” circuits, those in the middle for the double spiral.

A Baltic wheel has a bigger, empty center and a short second exit. This is already a double spiral, yet without more twists. Both accesses are normally separated by an own intermediate piece, a sort of shoehorn.

The pattern for the layout is the same one for both labyrinth types. The tool to produce the layout is also the same. The number of the circuits in all can be different, nevertheless.

Here it is only about the method. The geometrically correct construction is another thing again. There are already several posts in this blog about that.

There is no seed pattern like we have it for the well-known classical labyrinth. However, there is a basically very simple method to draw such a labyrinth or to lay it directly with stones or to scratch it in the sand.

A step-by-step instruction should show it. The boundary lines of the labyrinth are drawn, the path runs between the lines.

Step 1

Step 1

Step 1: I draw half a curve upwards, from the left to the right.

Step 2

Step 2

Step 2: I jump a little bit to the left, make a curve downwards to the left, walk round the first curve and land to the right of the preceding curve.
This would already be the center of the Baltic Wheel or the middle of the smallest possible Wunderkreis.

Step 3

Step 3

Step 3: Nevertheless, the double spiral should become bigger. Hence, I jump again a little bit to the left at the end of the first curve in green, make an other curve downwards to the left and walk again round the preceding curves.
Thus I could continue any desired. There must be left on the right side, however, always two free curve ends. With that the double spiral would be finished inside the Wunderkreis.

Step 4

Step 4

Step 4: Now I must add at least three semi-circular curves round the previous lines.
If I want to have a bigger labyrinth, I can add more lines in pairs. There must however be an odd number of curves.
In our example we now have on the left side three free line ends, and on the right side five.

Step 5

Step 5

Step 5: Now I connect on every side the innermost and the outmost lying free line in such a manner that in between an access is possible. This is to be continued (here only on the right side) so long as on every side only one single line end is left.

Step 6

Step 6

Step 6: The both on every side lying free line ends are extended forwards. They represent the both lower turning points.
The labyrinth is finished.

Finally we will check out if the drawing is correct. We go in between the lines, turn to the right or to the left and must come again to the starting point. If not, something must be wrong.

Best try it out yourself, with a pencil on a sheet of paper. Wishing you success.

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Among the Wunderkreise there are some variations:

  • Some with two entries like the Zeiden Wunderkreis
  • Some with one access, but a bifurcation such as the Russian Babylons and the examples of Kaufbeuren or Eberswalde
  • Some with a nearly perfect double spiral like the Zeiden Wunderkreis
  • Some with a “pulled apart” double spiral such as the Russian Babylons, the example of Eberswalde and some Swedish and Finnish examples

The Babylonian Wunderkreis

Wunderkreise are compound labyrinths which are constructed from curves around different central points. Both lower turning points are proper for the “labyrinthine” circuits, the ones in the middle for the double spiral.
The double spiral in the Zeiden Wunderkreis is made from two centres lying side by side, and with it a total of only four centres the whole Wunderkreis can be constructed.

Here a Swedish example with a pulled apart double spiral from the book of Hermann Kern:

Petroglyph on the Skarv Island (Sweden)

Petroglyph on the Skarv Island, Source: Hermann Kern, Labyrinthe, 1982, fig. 584 (German edition); Photo: Bo Stiernström, 1976

A geometrically correct construction for a Wunderkreis with pulled apart double spiral requires more centres. Thus I receive for the Russian Babylons a total of six centres.

A sort of prototype with the dimension between axes of 1 m should serve as example. All values are thereby scaleable and differently big labyrinths can be constructed.

Construction elements

Construction elements

Best of all one begins by defining M1. After that one determines the direction of the perpendicular bisectors of the sides, and then constructs step by step the remaining mid points M2 to M6 through building the intersection of the triangle sides from two known points. All thereto necessary measurements are contained in the drawing.

The main dimensions

The main dimensions

The radii refer in each case to the middle axis of the boundary lines. The way runs between these boundary lines and, hence, is the empty space between these lines.

The different radii

The different radii

Here are the above shown components in one drawing as a PDF file to look at, to print or to copy.

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The Babylons are surely related to the widespread Troy Towns of the European North. However, they look a little bit different.
Directly after the entrance there is a bifurcation and therefore it is possible to go on in two directions. And then often there is no real middle, but rather you are headed back in a double spiral.

The Troy Town of Visby (Gotland Island, Sweden)

The Troy Town of Visby (Gotland Island, Sweden), Source: Ernst Krause, Die Trojaburgen Nordeuropas, 1893, fig. 1, p. 4

However, how could they have developed?
Numerous stone labyrinths have survived down to the present day in Fennoscandia. The Babylons are to be found particularly in the eastern area, from Finland up to the Russian Kola Peninsula. Often they are situated near the coast and on islands. The natives of Northern Europe, the Sami, settled here. It is possible that the Babylons deal with the traditional Sami religion.
They have presumably originated from the 13th century on until our times. And they were built in the same way: With stones fist-sized to head-sized laid down on the ground.

However, why do the Babylons look different and do not follow the well-known seed pattern with cross, angles and four dots? Much Scandinavian Troy Towns have eleven circuits and have been laid after the enlarged seed pattern.

The 11-circuit Cretan (Classical) labyrinth with the seed pattern of the cross, the four double angles and the four dots

The 11-circuit Cretan (Classical) labyrinth with the seed pattern of the cross, the four double angles and the four dots, on the right in a round shape

Thereby divergences and variations appeared. This can happen quite easily through this construction method.
Thus there are Swedish Troy Towns with the open cross which enables to take two directions to reach the middle, and to organise a race, e.g. This is why these also often are called “Jungfrudans” or “Jungfruringen”.

9-circuit stone labyrinth (Jungfruringen) at Köpmanholm (Sweden)

9-circuit stone labyrinth (Jungfruringen) at Köpmanholm (Sweden), Source: © John Kraft, Die Göttin im Labyrinth (1997), fig. 7, p. 26 (German edition)

In the seed pattern for this labyrinth double angles only were used in the lower area. So we have 9 circuits.

Here the layout for a 11-circuit labyrinth:

The 11-circuit Cretan (Classical) labyrinth, on the right with open cross

The 11-circuit Cretan (Classical) labyrinth, on the right with open cross

In the report of Budovskiy I found a graphics (from 1973?) by Prof. Kuratov who has carried out a division of labyrinths and wanted probably show how the Babylon developed (see the sketched line in the graphics).

The table of Prof. Kuratov

The table of Prof. Kuratov

In the first column a sort of principle is to be seen. As first the whole Cretan labyrinth. In the second the left-handed spiral, in the third the right-handed spiral, then the double spiral and below circles.
In row Ia we see the Cretan type in different variations.
In row Ib the open cross and a decreasing middle.
In row II a right-handed spiral and the faulty stone setting discovered by Karl Ernst von Baer (1792 – 1876) in 1838 on the island of Wiehr.
In row III the Babylon with the double spiral.
In row IV some multiple-arm labyrinths which remind of the medieval labyrinths.

The open cross occurs several times under the Scandinavian labyrinths. Besides, the empty middle sometimes becomes smaller and then even slides under the two upper turning points. Finally, it is only indicated and then left out completely.

The drawing of John Kraft shows this:

The Troy Town of Nisseviken (Sweden)

The Troy Town of Nisseviken (Sweden), Source: graphic by © John Kraft in Gotländskt Arkiv 1983 on Gotlands trojeborgar, p. 87

I have found in a report about the Babylons on WeirdRussia, beside numerous photos, also this graphic :

Stone setting on the Bolshoi Zayatsky Island

Stone setting on the Bolshoi Zayatsky Island

The middle exists next to nothing. It is rather a niche or a widening of the way. In this area small stone heaps are sometimes stacked up. Should they show the gate to the underworld or the belly of the snake? The ends of the boundary lines are thickened. This is quite easy to make with some more stones.
The labyrinth has changed its meaning, with this its appearance and became the walk-through labyrinth.

Here the layout in geometrically correct form:

 

Babylon Solovki

Babylon Solovki

Presumably most of the Babylons correspond to this shape.

On this photo one can recognise very well the alignment.

There is a graphic with a little “rounder” double spiral in the table of Prof. Kuratov and in Vinogradov’s report which I have still shown in my last post (see below).

There are  obviously some among the Finnish stone settings which look rather so.

Graphics of a Babylon according to Vinogradov

Graphics of a Babylon according to Vinogradov

According to most of the photos the Babylons doesn’t look exactly like this. The entrance is narrower and has a short straight piece.

Actually, one must consider them as a Wunderkreis. Even if they don’t have such a perfect double spiral like the Zeiden Wunderkreis. The Wunderkreise of Kaufbeuren or Eberswalde matches more likely the Babylons.

How could one call this type? In the last post I had suggested: Babylonian Wunderkreis. However, now I tend rather to Sami Wunderkreis because it developed in the cultural area of the Sami and probably was used in the cult of the dead.

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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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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.

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