Posts Tagged ‘classical labyrinth’

Or differently asked: Can I transform a classical labyrinth into a Babylonian visceral labyrinth?

Therefore we should first see the differences; and then the interlinking components.

As an example I start with the best known classical labyrinth: The 7 circuit Cretan labyrinth.

The 7 circuit labyrinth

The 7 circuit Classical labyrinth, on the right the complementary to it

It has a center and an entrance. There is only one way in. In the middle I am at the aim and at the end of the way. To leave I must turn and take the same way in reverse order.

Among the Babylonian visceral labyrinths one can distinguish two main groups. One are more round and devoured into each other, while in others the loops are arranged row-shaped.

Here as an example the labyrinth E3384_r8 on a clay tablet from Tell Barri (Syria) (for more, please see related posts below).

A Babylonisn visceral labyrinth

A Babylonian visceral labyrinth with 10 circuits and two entries

In the visceral labyrinth I have two entries and no real center. Nevertheless, the way leads through all of the loops to the other access. It is a walk-through labyrinth.

The circuits here are numbered from the left to the right, while in the classical labyrinths they are numbered from the outside inwards. “0” stands for the outside, in the classical labyrinth the last figure for the center.

Every labyrinth is designated by a row of numbers, the circuit sequence or the path sequence. This is the order in which the circuits will be run one by one.

The connecting element therefore is the circuit sequence. Hence, we must construct “row-shaped” walk-through labyrinths from the circuit sequence of the classical labyrinths.

At first we take the 7 circuit labyrinth as shown above. We use the circuit sequence and connect the circuits arranged in row accordingly. The second “0” indicates the walk-through labyrinth.
Then this looks as follows:

Das 7-gängige Labyrinth als Eingeweidelabyrinth

The 7 circuit classical labyrinth as visceral labyrinth, on the right the complementary

We make this still for some more classical labyrinths.

Das 3-gängige Labyrinth

The 3 crcuit labyrinth, on the left the original, on the right the complementary to it

The original is developed from the meander and is also called Knossos labyrinth. The right one is developed from the “emaciated” seed pattern. However, is at the same time complementary to the Knossos labyrinth. Under the walk-in labyrinths the visceral walk-through labyrinths.

A 5 circuit labyrinth:

Das 5-gängige Labyrinth

A 5 circuit labyrinth, on the right the complementary

There are still other 5 circuit labyrinths with an other circuit sequence. But, in principle, the process is the same one.

The shown examples were all self-dual labyrinths.

Now we take a 9 circuit labyrinth. There are more variations:

Das 9-gängige Labyrinth

A 9 circuit labyrinth in four variations

And here the corresponding visceral labyrinths:

Die Eingeweidelabyrinthe

The visceral labyrinths

Here the 11 circuit labyrinth with the corresponding visceral labyrinths:

Das 11-gängige Labyrinth

The 11 circuit labyrinth and its complementary

This one is self-dual again. Therefore there is only one complementary version to it.

Here the 15 circuit labyrinth:

Das 15-gängige Labyrinth

The 15 circuit labyrinth and its complementary

This is also self-dual.

If we compare these newly derived visceral labyrinths to the up to now known historical Babylonian visceral labyrinths, we can ascertain no correspondence. Maybe a clay tablet with an identical labyrinth appears somewhere and sometime?

So far we know about 21 Babylonian visceral labyrinths as row-shaped examples in most different variations.

For comparison I recommend the following article with the overview.

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Hermann Kern is writing in his book Through the Labyrinth (Prestel Verlag, Munich) on page 23 about the principles of form:

Every labyrinth consists of lines that may be construed as a sort of ground plan; they form a sophisticated pattern of movement that requires considerable powers of the imagination to grasp. By trying to envisage walking the path between the lines, one can begin to comprehend this pattern.

Quoting this, I don’t want to deter someone, but make clearly that the employment with the labyrinth can be absolutely demanding. And I would like to assist for a better understanding.

From all one can “generate” a labyrinth, more exactly said: the way in a labyrinth. Since the meander is Ariadne’s thread (just the way) in linear form.
On looking more carefully one recognises some small differences. They are formed by mirroring the “basic form” either in horizontal or vertical axis. One can distinguish four different variations. In the following drawing this can be understood with the help of the colours and figures:

I can “read” the meander from left to right or from right to left. Accordingly to that is the situation of the entrance.

How do I make a labyrinth out of the meander? Or said a little more sophisticated: What code is hidden in the meander that leads me to the labyrinth?

I try to make the “deciphering” as easily comprehensible as possible. Therefore the colours and the figures shall serve as help. So one can pursue the way of the single segments.

Rotated meander

Rotated meander

First I turn the meander with the access below left from the above drawing about 90 degrees to the left.
The “secret” in the meander is the arrangement of the lines. They are numbered from “0” to “8”. “0” stands for outside, beginning of the line, init. “8” stands for inside, end of the line, middle, center, goal, target, aim. These line segments are also marked with different colours.
Now I read the order in which these segments will be passed through. And, true readers of this blog know it, this will give me the path sequence (line sequence, circuit sequence, level sequenc) for the labyrinth. It is: 0-3-2-1-4-7-6-5-8.
I can also derive the changes of direction from it. So whether it goes to the left or to the right, outwardly or inwards.

I pull apart this rotated meander crosswise. The labyrinth will be presented as a diagram. Of course the lengths of the single line segments are distorted, do not correspond to the original ones or the new lengths. But it does not depend on it at all. It is only important in which direction a line is running. For it is a pattern. Maybe it is difficultly to understand, above all the situation of the entrance and the center. In the real labyrinth they are situated near together and not as in the pattern on the right or left side outside.

The diagram

The diagram

I imagine this rectangle always as a pulled apart ring or tyre. If I cut the back side of this ring in the middle and lay both outer ends side by side, the entrance will be situated on the left side and the center on the right one.
Maybe one can recognize that better in the lower drawing? If I pursue the numbered lines (3-2-1-4-7-6-5-8) I alternately have to leave one side and enter on the other side again. The best bet is to try out.

The split diagram

The split diagram

Because I can deduce the right path sequence for the labyrinth (Ariadne’s thread) from the meander, I can draw the labyrinth by only using this path sequence. I do not need the well-known seed pattern to draw the labyrinth (the walls).
The labyrinth matching to the meander and the diagram looks as follows:

The left-hand classical labyrinth (Ariadne's thread)

The left-hand classical labyrinth (Ariadne’s thread)

Here in square shape:

The square classical labyrinth

The square classical labyrinth

Which meander generates now this left-hand labyrinth? From the above shown four versions the one with the access below left and the other with the access above right. Why? Because the circuit 3 (yellow) turns to the left after passing through 0 (grey).

However, in the meander versions with the access below right and the access above left circuit 3 turns to the right first. Consequently the labyrinth generated from them must also look different, namely as follows:

The right-hand classical labyrinth (Ariadne's thread)

The right-hand classical labyrinth (Ariadne’s thread)

However, this is nothing else than the vertically mirrored left-hand labyrinth.
Two versions of the classical 7 circuit labyrinth can be derived from the four possible versions of a meander, suitable for a labyrinth.

However, in the end the labyrinth should be also shown in such a way as it many know: With the representation of the boundary lines (the walls). They are held in black. The way, Ariadne’s thread coloured in the drawings before, is the free space between the lines. The boundary lines cross and have a beginning, here even four. This form can be easier generated from the seed pattern.

The left-hand classical labyrinth (walls)

The left-hand classical labyrinth (walls)

If one makes the ways in all circuits of the same width, the usually central cross will change to the the diamond-shaped “fontanel”.

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On Saturday 4th of August, 2012 at the the labyrinth congress in Hofkirchen i. M., the morning was dedicated to the labyrinth of transformation. We had first a short introduction to the origination process of this impressive labyrinth made of granite from the Mühlviertel (Austrian district, where Hofkirchen is situated). After that we explored the labyrinth ourselves, combined with a small ritual.

The layout of the stone labyrinth

The layout of the stone labyrinth

Here some information from a very good made tablet beside the labyrinth:



Here some pictures from the labyrinth walk:

Please try also to use the carousel for looking the pictures in full screen mode. Click inside any picture. Then you can scroll forwards and backwards. To return to this post click into the black surface or press the “Esc” key on your keyboard.

Who wants to visit the labyrinth, has several possibilities:

  • Look for information on the website Labyrinthe Hofkirchen
  • Ask anyone on site, because everybody in Hofkirchen knows the way
  • Orientate and navigate on one’s own. Hikers and bikers will reach it directly, drivers must get out before. Here the geographical position of the stone labyrinth: 48 28 38.9 N, 13 50 0.6 E

Or take a look on Google Earth? The labyrinth is not to be seen as yet. But maybe in some years when the satellite images are replaced?
The labyrinth is approximately in the middle of the image, on a clearing in the right upper corner.

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To draw the labyrinth from the basic pattern, still fascinates everybody which does it the first time. There is the basic pattern for the boundary lines (the walls) and since 2010 also the basic pattern for the path, Ariadne’s thread.

However, this is not the only possibility. On exploring the meander I have generated labyrinths from different meander combinations, and have found well-known and new types unknown still up to now.
I have seen the meander as a source for the path sequence in the labyrinth. Since a labyrinth is defined above all by its path sequence, even tough not only.

When drawing freehand Ariadne’s thread I have discovered that there are sometimes several possibilities to change the direction of a circuit.

This inspired me to look for other variations for the well-known classical 7 circuit labyrinth with the meanwhile equally well-known path sequence 0-3-2-1-4-7-6-5-8.
And I have found three other labyrinth shapes with the same path sequence.

I have determined the basic pattern contained in it and the angular thread of Ariadne in form of the meander not until the labyrinth construction.

Here at first the familiar classical labyrinth in “pure form”:

The classical 7 circuit labyrinth

The classical 7 circuit labyrinth

The basic pattern for the walls is emphasized in color. Ariadne’s thread in diagram form shows that the path in the labyrinth is composed of two simple meanders (named type 4 by me).
The labyrinth has 7 circuits, four turning points and the path sequence 0-3-2-1-4-7-6-5-8.

In this variation the fourth circuit crosses the main axis and from the same path sequence as in the preceding labyrinth appears a new type:

A 7 circuit classical labyrinth with the 4th circuit crossing the axis

A 7 circuit classical labyrinth with the 4th circuit crossing the axis

The basic pattern is pulled apart and split. Ariadne’s thread is equally pulled apart, but both meander elements are clearly recognizable.
The labyrinth has 7 circuits, four turning points and the path sequence 0-3-2-1-4-7-6-5-8, however, quite an other shape.

Here the 7th circuit crosses the main axis and from the same path sequence a new type is generated:

A 7 circuit classical labyrinth with the 7th circuit crossing the axis

A 7 circuit classical labyrinth with the 7th circuit crossing the axis

The basic pattern is shifted again and split. Ariadne’s thread is changed, recognizable, however, the second element is mirrored.
The labyrinth has 7 circuits, four turning points and the path sequence 0-3-2-1-4-7-6-5-8, however, again quite an other appearance.

Now the 4th and 7th circuit crosses the main axis and from the same path sequence again a new type is produced:

A 7 circuit classical labyrinth with the 4th and the 7th circuit crossing the axis

A 7 circuit classical labyrinth with the 4th and the 7th circuit crossing the axis

The basic pattern is shifted and split. Ariadne’ s thread is changed, however, the two meander elements are recognizable.
The labyrinth has 7 circuits, four turning points and the path sequence 0-3-2-1-4-7-6-5-8, however, again quite an other appearance.

There are for the same path sequence four different shapes. It’s difficulty to name them correctly (and in short terms). Here one sees clearly that the information of the path sequence is not sufficient for the definition of a type.

Now one could ask, why there existed up to now no labyrinths of these types. From the modified basic pattern they are not easily to build, from the meander probably also not.

Considered closely, these three new variations doesn’t look especially nice. The components of square and circle do not make an appearance. The original, oldest and well-known version of the classical labyrinth is well-balanced and harmonious. There’s nothing like the good, old Cretan labyrinth. This shows up once more.

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The Roman Cellar of the hypo-bank of  Salzburg was the first station of the exhibition “In der Mitte sein” (Be in the center) of the artist Marianne Ewaldt. It was opened from the 15th to the 29th of June, 2012.

Marianne Ewaldt has put a labyrinth inside an octagon with mirrored walls. She was inspired by an idea sketch of Leonardo Da Vinci (1492 – 1519) which could not be realised, however, at his time.

It is an experience of own kind, to realize in such surroundings the middle of the octagon, of the labyrinth and his own middle. Since one finds himself often reflected, on no account restricted or depressed as one could maybe suppose. The space opens widely. It is another way in the labyrinth on the search to itself.

Try to use the carousel by clicking inside the first picture. You may return by clicking inside the black area.

The next opportunity to walk the labyrinth inside the octagon will be at Hofkirchen (Austria) during the next labyrinth congress for the German-speaking area from August 2 to 5, 2012.

Note from October 16, 2012: The octagon is now in a museum, called “Villa sinnenreich” at Rohrbach (Upper Austria), where it can be visited during the opening times of the museum.
Here is a link to the museum.

For more pictures please go to my website mymaze to the photo gallery.

More information about the Salzburg ceramic and land art artist Marianne Ewaldt on her website.

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or also

The skew / crooked / distorted / deflected / sloped / switching Labyrinth

Seen with the eyes of a geometer and labyrinth builder (optional: designer or somewhat sophisticated: experimental Labyrinthologist)

The Classical Labyrinth

Here the classical labyrinth, composed after the well known basic pattern with the cross, four dots and four angles in between. Arranged in a square.

The classical labyrinth with constant paths

The classical labyrinth with constant paths

From this square the whole labyrinth is developed, connecting all elements  in curved lines together. So it is a synthesis of square and circle. And all 5 centers of this curved lines are located inside the square and their bow-shaped  pieces (semicircles and quarter circles) are connected without sharp bends. So the labyrinth figure with her boundary lines is built.
If one wants a walkable labyrinth with constant path widths, the central source cross withdraws and a rhombus-shaped figure (fontanelle) remains.
If one looks at the layout of the paths, one recognises that the entry axis, the middle axis, the central axis are all lying in different levels. The entry axis does not lie in a line with the path axis which leads into the middle. There is a sort of center and middle, they have passed away of each other. Only in the Roman labyrinth they coincide.
Or differently expressed:
A labyrinth is not symmetrical, although it looks steady.
A labyrinth is no spiral, although the ways writhe.
A (classical) labyrinth is not a figure of a circle, although it is built of arcs.

Here you will get the drawing for a classical labyrinth as a PDF file (in German) to look at / to print / to download / to copy.

The Knidos Labyrinth

To walk a labyrinth with groups a bigger middle is often wished.
The first time in history such a labyrinth could be seen on a graffito which was found on a stone block on the peninsula Knidos in today’s Turkey in excavations of old Roman structures and can be dated to the Byzantine epoch.

The Knidos Labyrinth

The Knidos Labyrinth

The center for the middle jumps quasi out of the square (virtually an ovulation).
The geometrical conversion is more difficulty now. If one maintains the four centers arranged inside the square, the different axes move in different distances and one gets some bigger and smaller segments (like cake pieces) from the previous semicircles and quarter circles. All in all the labyrinth shape becomes more round.

Here you will get the drawing for a Knidos labyrinth as a PDF file (in German) to look at / to print / to download / to copy.

The coaxial Knidos Labyrinth

If one liked to have the axis of the last path piece and the center of the middle on the same line, both right centers inside the square move a little bit upwards and to the left. The square changes to a rhomb and the cake pieces will change as well.

The coaxial Knidos labyrinth

The coaxial Knidos labyrinth


Here you will get the drawing for a coaxial Knidos labyrinth as a PDF file (in German) to look at / to print / to download / to copy.

The centred Knidos Labyrinth

Should all axes lie on a line now (as for example does the Santa Rosa Labyrinth), the 4 centers inside the square move even more. Consequently the cake pieces and the fontanelle. The original 4 centers have totally contorted and lie crooked within the labyrinth figure.

The centred Knidos labyrinth

The centred Knidos labyrinth

Here you will get the drawing for a centered Knidos labyrinth as a PDF file (in German) to look at / to print / to download / to copy

What labyrinth shape do you like best?

This depends of course also at which place the labrinth is situated and which purposes it serves, what should be stated with it and what would be personally important.
Other variations are still possible, one receives the easiest ones by mirroring the figure in a vertical axis.
One could look at the stages of development of the classical labyrinth to the centered Knidos labyrinth as a change of the square and rectangle to the circle. Then the output stage could be the Chartres labyrinth where the circle and the middle is even more accentuated and where the cross form is expressed in the whole labyrinth.

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In a comment I got the reference to a presentation, in which the labyrinth plays a role.

Title: Sarirayantra or “Das Band der Flut”  or “Der Allursatz der Flut”. Author is Mar Cel.

The presentation can be seen on Vimeo (duration 22 minutes).

You may select between a QuickTime a presentation, Apple Keynotes presentation and different printing versions.

The labyrinth is placed into a quite large and cosmic connection. One can see it in such a way, must however not. It will be the best to look yourself.

Annotation: All the text is in German.

The golden ratio

The golden ratio

© Mar Cel (Anangavajra Tamratejas) 2009

For the following terms, which emerge all, a resuming view cannot harm. Therefore a link is specified (mostly to Wikipedia) for all of them.

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