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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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In part 1 (see Related Post below) about the simplified seed pattern I only have spoken of the enlargement of labyrinths.

The seed pattern

But of course the number of circuits also can be reduced by this way. This is possible for all labyrinths built from this seed pattern, as well as for all containing this pattern. I would like to call them compounded labyrinths.

For me this are the Indian Labyrinth, the Baltic Wheel and the Wunderkreis. They all have only two turning points, however, the middle is formed in each case differently.
The Indian Labyrinth (Chakra Vyuha) contains a spiral, the Baltic Wheel has a big empty middle and a second access, the Wunderkreis contains a double spiral and also has the second access.

Here the Indian Labyrinth which can be generated through a seed pattern contained in a triangle:

The Indian Labyrinth

The Indian Labyrinth

The Indian Labyrinth with two more circuits:

The enlarged Indian Labyrinth

The enlarged Indian Labyrinth

Here the Baltic Wheel. The middle section is constructed in a special way. But the circuits round the two turning points can be increased or decreased in pairs.

The Baltic Wheel

The Baltic Wheel

The Baltic Wheel with two less circuits:

The downscaled Baltic Wheel

The downscaled Baltic Wheel

The Wunderkreis has a double spiral in the middle section. The double spiral can have more or less windings (not shown here). But the typically “labyrinthine” circuits round the two turning points can be influenced as mentioned above.

The Wunderkreis

The Wunderkreis

The Wunderkreis with two less circuits:

The downscaled Wunderkreis

The downscaled Wunderkreis

In the quoted statements I would like to show that there is a “technology” through that one can influence the size of a labyrinth.

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At the end of the last post (see related posts) we were left with the following problem. If we number the segments consecutively, we obtain a unique seqence of segments. However it can not be directly seen in the sequence of segments which circuit is encountered by the pathway. If we number the segments by circuits, the sequence does indicate which circuit is encountered. However it then looses the uniqueness.

Now there is a possibility to combine the numbering. That means to write a number for the circuit first, then a separator and then a number for the segment. In the example of the labyrinth by Valturius this looks as follows (fig. 1).

nummerierung-us

Figure 1. Numbering by Circuits and Segments

 

The labyrinth has four circuits and three arms, and thus also three segments per circuit. The first number indicates the circuit, the second indicates the segment. This numbering provides some kind of coordinates for the various segments.

Let us now write the sequences of segments for the alternating and non-alternating labyrinths from the last post using this numbering.

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Figure 2. Sequences of Segments of the Alternating and Non-alternating Variants

Both variants have their own unique sequences of segments. In each element of the sequence of segments it can be identified which circuit and which segment is encountered by the path. Such a sequence of segments can be easily generated and memorized. A shortcoming of this numbering is that each element is composed of two figures and a separator. Furthermore the elements must be clearly separated from each other. Therefore this sequence of numbers requires more digits and more space.

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When I dealt with the Knossos labyrinth it has struck me that the seed pattern can be simplified very easily. It can be reduced to three lines and two dots. To draw the labyrinth they are connected just as we do it for the classical labyrinth. For more information please see the Related Posts below.

Now this seed pattern with the two turning points can be extended in a very simple way, just by adding more lines in pairs.
seed pattern

The bigger labyrinths have more circuits, however, maintain her basic structure. And, nevertheless, these are own types, because they have another path sequence than the 7-, 9-, 11-, 15- etc. circuit  classical labyrinths. But they are not known, neither among the historical, nor among the contemporary labyrinths. Because they are too easy? Besides, the lines have quite a special rhythm. A closer look can be worthwhile.
The 3 circuit labyrinth of this type first appeared about 400 B.C. on the silver coins of Knossos:

The Labyrinth Type Knossos

The Labyrinth Type Knossos

The circuits are numbered from the outside inwards from 1 to 3. The center is marked with 4. The blue digits labels the circuits inside out. The path sequence is 3-2-1-4, no matter which direction you take. Through that a special quality of this labyrinth is also indicated: It is self-dual.

What now shall be the special rhythm? To explain this, we look at a 5 circuit labyrinth of this type:

The 5 circuit Knossos Labyrinth in the Cretan Style

The 5 circuit Knossos Labyrinth in the Cretan Style

The path sequence is: 5-2-3-4-1-6. At first I circle around the center (6) on taking circuit 5. Then I go outwardly to round 2, from there via the circuits 3 and 4 again in direction to the center, at last make a jump completely outwards to circuit 1, from which I finally reach the center in 6.


Here a 7 circuit labyrinth in Knidos style:

7 circuit Labyrinth in Knidos style

7 circuit Labyrinth in Knidos style

The path sequence is: 7-2-5-4-3-6-1-8. It is also self-dual. The typical rhythm is maintained, the “steps” are wider: From 0 to 7, from 7 to 2, and finally from 1 to 8 (the center).

Here a 9 circuit labyrinth in circular style:

9 circuit Labyrinth in circular style

9 circuit Labyrinth in circular style

The path sequence is: 9-2-7-4-5-6-3-8-1-10. The step size is anew growing. This labyrinth is self-dual again.

This example exists as a real labyrinth since the year 2010 on a meadow at Ostheim vor der Rhön (Germany):

9 circuit Labyrinth in circular style at Ostheim vor der Rhön (Germany)

9 circuit Labyrinth in circular style at Ostheim vor der Rhön (Germany)

To finish we look at a 11 circuit labyrinth in square style:

11 circuit Labyrinth in square style

11 circuit Labyrinth in square style

The path sequence is: 11-2-9-4-7-6-5-8-3-10-1-12. And again self-dual.

I think, the method is clear: We add two more lines more and we will get two circuits more. So we could continue infinitely.
The shape of the labyrinth can be quite different, this makes up the style. The path sequence shows the type. And for that kind of labyrinth we always have only two turning points.

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This labyrinth exists since 2014. I still have written about a visit of the health garden containing it in my personal Blog (see Further Link below). Today we will look at the labyrinth itself.

Thus is the plan:

The Roman labyrinth

The Roman labyrinth

It is a serpentine-type Roman labyrinth with four sectors. The whole diameter amounts to 15 m, the middle has a diameter of 1.40 m. The ways are 40 cm wide and paved with granite stones. They are separated of each other by a 50-cm-wide grass verge. The whole way through the 7 circuits in the 4 sectors to the center amounts to about 182 m. The entrance of the labyrinth lies on the right beside the main axis. The dividing stripes of the single quadrants lie on a cross.

Some photographic impressions:

There are two videos on YouTube, here the first one:

And here the second:

In the meantime, I have considered what one could have made better in a “labyrinth-technically” way. Since the idea in itself of a Roman labyrinth in the middle of the health garden seems not to be so good realized.

The last piece of the path arriving the center should always lie on the central main axis. If one makes the middle a little bigger, one receives above all longer and steadier path segments around the middle. If one wants to reach this and maintain the whole diameter of 15 m, one can make the paths and the dividing stripes each 40 cm broad. Then the center would have a diameter of 3.2 m.
One could have built a better Labyrinth at the same place and with the same costs.

Here the layout drawing:

The layout drawing

The layout drawing

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Further Link (in German)

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Wishing all visitors of this Blog a Merry Christmas and a Happy New Year!

Classical 7 Circuit Christmas Tree Labyrinth

Classical 7 Circuit Christmas Tree Labyrinth

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In my last post I have shown the sequence of segments in labyrinths with multiple arms. This is unambigous. But as a disadvantage it does not indicate directly which circuit is encountered by the pathway.

Now it is also possible to keep the partition in segments but only number the circuits. This allows to indicate directly in the sequence of segments, which circuit is visited by the pathway. Thus the same number may repeatedly occur in this sequence. This works well in many cases but may also leed to problems. In the labyrinth I had shown in my last post the problem does not occur. Therefore I will illustrate it here with an other example. For this I chose the labyrinth by Valturius as this is a small, understandable example (Fig. 1).

valturius

Figure 1. Labyrinth by Valturius. Source: Kern 2000, fig. 315, p. 179.

This labyrinth from a military manuscript by Robertus Valturius of the 15th century has three arms and four circuits. (Please note, that the arms are not proportionally distributed. This, however, has no influence here. I therefore use a proportional distribution for reasons of simplicity.)

num_valturius

Figure 2. Numbering of the Segmente: Left Image by Segment, Right Image by Circuit

Figure 2 shows in the left image the partition and numbering by segments I had already used in my last post. The right Image shows the same partition of segments although numbered by circuits only. As the labyrinth has four circuits, there are 12 segments.

The labyrinth by Valturius is alternating. However there exists a non-alternating labyrinth with the same level sequence. And this brings us back to the problem.

sf_valturius

Figure 3. Sequences of Segments Numbered by Segments

Figure 3 shows the alternating labyrinth by Valturius (left image) and the non-alternating variation (right image). They show two different courses of the pathway. These are also correctly represented by the two different sequences of segments. Both sequences of segments are similar for the first 9 segments: 1 4 7 8 5 2 3 6 9 … The sequences of the three last segments, however, are different. In the labyrinth by Valturius the sequence continues with segments ……… 12 11 10. On the other hand, the sequence of segments in the non-alternating variation is ……… 10 11 12.

If, however, we number the segments by circuits, we lose the uniqueness.

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Figure 4. Sequences of Segments Numbered by Circuits

Figure 4 shows the same labyrinths as fig. 3. But with their segments numbered by circuits. Both variants have the same sequence of segments 1 2 3 3 2 1 1 2 3 4 4 4. So here we can always identify in the sequence of segments, which circuit is encountered by the pathway. However, for the same sequence of segments there may exist multiple (in this case two) different courses of the pathway. The same problem occured already in the level sequence of one-arm labyrinths.

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