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On my own behalf

Welcome to the Labyrinth

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

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

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

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

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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

Related Posts

It is known that there are 8 alternating labyrinths with 1 arm and 5 circuits (see “Considering Meanders and Labyrinths”, related posts, below). Of these, four are not self-dual. These four all are in a relationship to each other via the duality and complementarity (see “The Complementary versus the Dual Labyrinth”, related posts, below). The other four labyrinths are self-dual.

I had already pointed to the relationship between complementary and self-dual labyrinths (see “The Complementary Labyrinth”, related posts, below). Here I want to elaborate on it further. For this purpose I use the same form of diagram I had already used in my previous post (see “The Complementary versus the Dual Labyrinth”). I also use the same numbers of the labyrinths according to the numbering of Arnol’d’s meanders (see “Considering Meanders and Labyrinths”), that underlie them.

Figure 1. Labyrinths 1 and 6

The first of the Arnol’d’s labyrinths, number 1, is self-dual. In the diagram, the dual is situated in the same row, the complementary in the same column with the original labyrinth. The dual of number 1 is again number 1 (what actually is the meaning of selfdual). The complementary of number 1 is number 6. And – of course – is the dual to the complementary again number 6. So in the case of self-dual labyrinths, we only captured two different labyrinths, whereas it were four in the case of not self-dual labyrinths.

Thus, two more labyrinths are still missing. We need another diagram to capture labyrinths number 3 and number 8 (fig. 2).

Figure 2. Labyrinths 3 and 8

And, indeed, these two are complementary to each other. So in self-dual labyrinths, only two different labyrinths are in a relationship to each other.

Here the question arises: Do there also exist self-complementary labyrinths? Up to now we have not yet found such a labyrinth. So let us remember, what self-dual imples. The patterns of the original and self-dual labyrinths are self-covering. In fig. 3 I show what that means. The two patterns in the same row are dual. If we shift them together, we can easily see, what I mean.

Figure 3. Self-dual patterns are self-covering

Thus, self-complementary would imply that the original and complementary pattern would also be self-covering.

Figure 4. Complementary patterns are not self-covering

Fig. 4 shows, that even though there is a certain similarity between these two patterns, they are not self-covering. In my opinion there are no self-complementary labyrinths. This is because vertical mirroring with uninterrupted connections to the entrance and center modifies the sequence of circuits. This, however, woult have to remain unaltered.

Related Posts:

What does I mean by “Indian labyrinth”? Therewith I understand at first a simple 3- or more circuit labyrinth (round two turning points) with a spiral in the middle. The spiral can have any number of lines. We therefore deal with a composite design.

The Labyrinth Society (TLS) classifies it as “Other Classical Seed Patterns”, whereby as subtypes are named the “Chakra-Vyuha Labyrinth” and the “Baltic Labyrinth”.

This type is still floating around, and is it as a decoration on a birthday tart, as recently did Lisa Gidlow Moriarty (USA):

Chakra Vyuha on a tart

Chakra Vyuha on a birthday tart, created and © Lisa Moriarty

Such a labyrinth can be generated from a seed pattern which is based on a triangle. It is also called Chakra Vyuha. However, there are also other seed patterns known (see related Posts below).

And therefore it is diffculty to classify all the types in a common typology, partly because they emerge quite differently in time and space.

I start with a simple labyrinth. It is found in Hermann Kern’s book and dates from the 12th century.

Chakra Vyuha

The Indian Labyrinth, Source: Hermann Kern, Labyrinthe (1982), fig. 602, p. 422 (German edition)

The Babylonian visceral labyrinth on a clay tablet with the number 9560 in the Vorderasiatisches Museum Berlin is about 2000 years older. The archeologist Ernst Friedrich Weidner (read more here) shows it in a report from 1917 as fig. 4:

The Babylonian visceral labyrinth

The Babylonian visceral labyrinth VAT 9560, fig. 4

This does not look as if it had been made from a basic pattern.

The visceral labyrinth in three moves

The visceral labyrinth in three moves

But it can be drawn in three moves. I begin in the middle, draw the spiral, make a loop outwards on the right side and shift in a bow to the left side (green line). Then I begin a new line inside the loop, round the preceding line and end the line at the underside of the spiral (blue line). The third line begins near the preceding line and shifts to the left (yellow line).

The Chakra Vyuha can be drawn the same way:

The Chakra Vyuha in two moves

The Chakra Vyuha in two moves

The path of the labyrinth, Ariadne’s thread, must be drawn in one move.

This can be done from the inside outwardly or also vice versa.


I had described a method to generate walk-through labyrinths from the type Wunderkreis with any desired circuits in the post “Variations on the Wunderkreis” (see related posts below).

This method, easily modified, can be also used to generate the composite labyrinths with spirals from any desired twists and simple labyrinths with three and more circuits.

Once again briefly the principles:

I begin in the middle and draw a spiral with at least one, however, also any desired turns. The boundary lines are colored in green, the path (Ariadne’s thread) in brown.

Round the spiral I add the desired number of labyrinthine circuits, at least three up to more (endlessly). But always an odd number.

From the outside inwards I draw the loops (in yellow). Because I must have an odd number of line ends for the boundary lines on every side, I begin or finish one line at the underside of the spiral.

In order to draw the boundary lines the middle free line inside the loops is extended forwards (in red).

In order to draw Ariadne’s thread I extend the most internal line forwards on the side with the odd number of line ends (in red). The remaining free line ends are connected in loops (in yellow).

In the last example I turn one more “lap of honour” (in black) around the whole. So I may produce with the right number of circuits the  historically verified Windelburg of Stolp.

The Windelburg of Stolp

The Windelburg of Stolp

The Windelburg of Stolp had a 3 circuit spiral and 15 labyrinthine circuits plus an additional circuit completely around.

How should one now classify the presented examples properly? One surely can not label all as Indian labyrinths. The Windelburg belongs rather to the Troy Towns and is also counted to the Baltic labyrinths. However, they all have the same pattern, belong to the same type.

To be able to build a labyrinth, one must bring it in a geometrically correct form. For this I choose the Windelburg, make less circuits and provide it in a layout drawing.

A new Windelburg

A new Windelburg

I present it as sort of prototype with 1 meter dimension between axes, a 2 circuit spiral and 9 labyrinthine circuits as a PDF file to look at, to print or to download.

Related Posts

In the last post I have presented the complementary labyrinth. I did this with the example of the basic type labyrinth. This is a self-dual labyrinth. The complementary is different from the dual labyrinth. This can be better shown using non-self-dual labyrinths. I want tho show this here and for this choose an alternating labyrinth with 1 arm and 5 circuits. As already shown in this blog, there exist 8 such labyrinths (see related post below: Considerung Meanders and Labyrinths). Of these, 4 are self-dual (labyrinths 1, 3, 6, and 8) and 4 are not self-dual (labyrinths 2, 4, 5, and 7).

I thus choose one of the non-self-dual labyrinths, nr. 2, and use the pattern of it. With the pattern, two activities can be performed:

  • Rotate

  • Mirror

Figure 1 shows the result of performing these actions with pattern 2.

Figure 1. Rotating and Mirroring of the Pattern

Rotation leads to the pattern of labyrinth 4
Mirroring leads to pattern 7

So we have already three labyrinths. Now it is possible to go even further. Rotating the dual again brings it back to the original labyrinth. However, the dual can also be mirrored. This results then in the complementary of the dual. And similarly, the complementary can be rotated, which results in the dual to the complementary.

Mirroring of the dual (pattern 4) leads to the complementary pattern of labyrinth 5
Rotation of the complementary (pattern 7) leads to the dual of it – which is also pattern 5.

Figure 2. Relationships

Figure 2 shows the labyrinths corresponding to the patterns. The labyrinths are presented in basic form (i.e shown with their walls delimiting the pathway) in the concentric style. All four non-self-dual alternating labyrinths with 1 arm and 5 circuits are in a relation of either dualtiy or complementarity to each other.

Related posts:

In my last posting I had introduced a method to draw the Wunderkreis. Besides, it was always about the boundary lines. However, the path (Ariadne’s thread) in the labyrinth can also be drawn with this method slightly changed then.

And of course numerous variations with differently many circuits can be generated for the double spiral and the labyrinthine windings.

Square Wunderkreis

Square Wunderkreis

Here in abstract once again the method:

  • I begin in the middle
  • Arc upwards from the left to the right, jump to the left, arc downwards
  • Path: Arc downwards, immediately following an arc upwards (closed line, like a recumbent “S”)
  • Jump to the left, curve upwards around the whole
  • Repeat this  as often as desired (on the right side there must always be two free ends which point down)
  • Then draw around the whole, beginning on the left, an odd number of curves (at least 3, until as much as you want)
  • Path: Extend both most internal lines down (maybe connect them)
  • Connect the free line ends on every side in loops
  • Boundary lines: Extend both most internal lines on every side inside the innermost loop

Sorry, this was a little longer. Maybe it is easier to understand the text together with the drawings. The different colours should help also. Best you try it yourself.

The labyrinth will be mirrored if one draws the first arc to the other direction.
One recognises the representation of the path by the fact that there are only two, perhaps only one line end (how it is also for the other types of labyrinths). If one sees four free line ends, the boundary lines are shown. Nevertheless, in the Wunderkreis the lines do not overlap as we see that in the classical labyrinth.

I have chosen known Wunderkreise as examples for the simplistic representation of the respective alignments.
In the related posts below you may find them all. As well as the step-by-step instruction.

Related Posts

If we turn the inside out of a labyrinth, we obtain the dual labyrinth of it. The dual labyrinth has the same pattern as the original labyrinth, however, the pattern is rotated by a half-circle, and the entrance and the center are exchanged. This has already been extensively described on this blog (see related posts, below).

Now, there is another possibility for a relationship between two labyrinths with the same pattern. In this kind of relationship, the pattern is not rotated, but mirrored vertically. Also – other than in the relationship of the duality – the entrance and the center are not exchanged. At this stage, I term this relation between two labyrinths the complementarity in order to distinguish it from the relationship of the duality.

Here I will show what is meant with the example of the most famous labyrinth.

This labyrinth is the „Cretan“, „Classical“, „Archetype“ or how soever called alternating, one-arm labyrinth with 7 circuits and the sequence of circuits 3 2 1 4 7 6 5, that I will term the „basic type“ from now on.

Figure 1.The Original Labyrinth

Figure 1 shows this type in the concentric style.

The images (1 – 6) of the following gallery (figure 2) show how the pattern of the complementary type can be obtained starting from the pattern of the original type.

Image 1 shows the pattern of the basic type in the conventional form. In image 2 this is drawn slightly different. By this, the connection from the outside (marked with an arrow downwards) into the labyrinth and the access to the center (marked with a bullet point) are somewhat enhanced. This in order to show, that when mirroring the pattern, the entrance and the center will not be exchanged. They remain connected with the same circuits of the pattern. In images 3 til 5 the vertical mirroring is shown, divided up in three intermediate steps. Vertical mirroring means mirroring along a horizontal line. Or else, flipping the figure around a horizontal axis – here indicated with a dashed line. One can imagine, a wire model of the pattern (without entrance, center and the grey axial connection lines) being rotated around this axis until the upper edge lies on bottom and, correspondingly, the lower edge on top. In the original labyrinth, the path leads from the entrance to the third circuit (image 3). With this circuit it remains connected during the next steps of the mirroring (shown grey in images 4, 5 and 6). After completion of the mirroring, however, this circuit has become the fifth circuit.The path thus first leads to the fifth circuit (image 6) of the complementary labyrinth. A similar process occurs on the other side of the pattern. In the original labyrinth, the path reaches the center from the fifth circuit. This circuit remains connected with the center, but transforms to the third circuit after mirroring.

Figure 3: The Complementary Labyrinth

In the pattern of the complementary labyrinth we can find a type of labyrinth that has already been described on this blog (see related posts). It is one of the six very interesting (alternating) labyrinths with 1 arm and 7 circuits. That is to say the one with the S-shaped course of the pathway.

So, what is the difference between the dual and the complementary labyrinth?

Let us remember that the basic type is self-dual. The dual of the basic type thus is a basic type again.

The complementary to the basic type is the type with the S-shaped course of the pathway.

By the way: In this case, the dual to the complementary is the same complementary again, as also the complementary of the basic type is self-dual (otherwise it would not be a very interesting labyrinth).

This opens up very interesting perspectives.

Related posts:

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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