What kind of labyrinth is this now?

At first sight it reminds of a medieval labyrinth, as it is the famous Chartres labyrinth. It has ten circuits in three sectors, in one these are eight. They will not be traversed one after the other, but reciprocally. And then it has two accesses: An entrance and an exit. It is a walk-through labyrinth as we know that of the Babylonian labyrinths. Hence, we have an own, new type. And we see the pathway in the labyrinth, Ariadne’s thread. This reminds us of the Greek myth of the Minotaur, which is to be combated like cancer here.

If the Babylonian visceral labyrinths served for the divination, here the labyrinth serves the medicine.

This reminds me of “Ancient Myths & Modern Uses“, the book about labyrinths of Sig Lonegren.

**Related Posts**

**Further Links**

- University of Michigan: Michigan News about the Labyrinth-Chip
- Research Journal Cell Systems: Report about the Labyrinth-Chip
- Science Alert: Report about the Labyrinth-Chip

Filed under: Design, Labyrinth, Report Tagged: Chartres labyrinth, visceral labyrinth, walk through labyrinth ]]>

First we write down the sequence of circuits for each of the four patterns. The patterns in the same column are complementary. Next we extract the sequences of circuits of dual labyrinths 2 and 4 and in the line below write the sequences of circuits of dual labyrinths 7 and 5. Now we can add the numbers below each other and will find that at each position they sum up to 6. This is 1 greater than the number of 5 circuits.

Now there is another relationship between the sequences of circuits. This is illustrated in figure 2.

The sequences of circuits of the dual-complementary labyrinths are mirror-symmetric. Thus, in this case, the labyrinths that are in a diagonal relationship to each other are considered. Labyrinth 5 is the complementary of the dual (4) and the dual of the complementary (7), respectively, i.e. the dual-complementary to labyrinth 2. This connection is highlighted by a black line with square line ends. The sequences of circuits of these labyrinths are also written in black color. If we write the sequence of circuits of labyrinth 2 in reverse order this results in the sequence of circuits of labyrinth 5 and vice versa (black sequences of circuits).

Labyrinth 7 is the complementary of the dual (2) and the dual of the complementary (5), i.e. the dual-complementary to labyrinth 4. This is highlighted by a grey line with bullet line ends. The sequences of circuits of these labyrinths are also written in grey. Also in this case it is true: the sequence of circuits of labyrinth 4 written in reverse order corresponds with the sequence of circuits of labyrinth 7 and vice versa.

**Related posts:**

Filed under: Design, Labyrinth Tagged: complementary, dual, dual-complementary, Sequence of Circuits ]]>

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.

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:

Here the 21 bigger tracings of the well recognisable specimens:

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.

**Related Posts**

- The Babylonian Labyrinth
- The Babylonian Visceral Labyrinth, Part 1
- The Babylonian Visceral Labyrinth, Part 2
- The Babylonian Visceral Labyrinth, Part 3

- How to Make a Babylonian Walkable Visceral Labyrinth
- How to Make a Babylonian Walkable Snail Shell Labyrinth
- A Babylonian 9 Circuit Visceral Labyrinth

Filed under: History, Labyrinth, Typology Tagged: Berlin labyrinth, double-spiral, Leiden labyrinth, visceral labyrinth, walk through labyrinth, Wunderkreis ]]>

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.

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).

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.

Thus, self-complementary would imply that the original and complementary pattern would also be 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:**

- Considering Meanders and Labyrinths
- The Complementary versus the Dual Labyrinth
- The Complementary Labyrinth

Filed under: Design, Labyrinth Tagged: Arnol'd, complementary, Labyrinth, meander, self-dual ]]>

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):

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.

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:

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

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 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 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.

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**

- The Indian (Chakra Vyuha) Labyrinth
- An Eleven-Circuit Cakra Vyuh Labyrinth
- How to simply make bigger and smaller Labyrinths, Part 2
- How to make a Wunderkreis or a Baltic Wheel
- Variations on the Wunderkreis

Filed under: Design, Labyrinth, Typology Tagged: Chakra vyuha, intestinal labyrinth, Stolp, Windelburg ]]>

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:

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

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 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:**

Filed under: Design, Labyrinth Tagged: complementary, dual, Labyrinth, mirroring, rotation ]]>

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

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**

Filed under: Design, Labyrinth, Typology Tagged: Babylonian Wunderkreis, baltic wheel, Eberswalde Wunderkreis, Kaufbeuren Wunderkreis, Rad in der Eilenriede, Transylvanian Wunderkreis, Zeiden Wunderkreis ]]>

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 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.

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:**

Filed under: Design, Labyrinth Tagged: basic type, complementary, dual, mirroring, pattern ]]>