How to make a Classical (Minoan) Labyrinth from a Medieval Labyrinth, Part 3

Quite simply: By leaving out the barriers in the minor axes. I have already tried this with the Chartres labyrinth some years ago. And in the last both posts on this subject with the types Auxerre and Reims. You can read about that in the related posts below.

Today I repeat this for the Chartres labyrinth. Here the original in essential form, in a concentric style.

The Chartres labyrinth

The Chartres labyrinth

The original with all lines and the path in the labyrinth, Ariadne’s thread. The lunations and the six petals in the middle belong to the style Chartres and are left out here.

Now without the barriers in the minor axes.

The Chartres labyrinth without the barriers

The Chartres labyrinth without the barriers

All circuits can be included in the labyrinth originating now, differently from the types Auxerre and Reims. The path sequence is: 5-4-3-2-1-6-11-10-9-8-7-12. We have eight turning points with stacked circuits. It is self-dual. That means that the way out has the same rhythm as the way in.

But this 11 circuit labyrinth is quite different from the more known 11 circuit labyrinth, that can be generated from the enlarged seed  pattern.
Since this looks thus:

The 11 circuit labyrinth made from the seed pattern

The 11 circuit labyrinth made from the seed pattern

The path sequence here is: 5-2-3-4-1-6-11-8-9-10-7-12. We have got four turning points with embedded circuits. It is developed from quite another construction principle than the Chartres labyrinth. However, it is self-dual.


Now we turn to the complementary labyrinth.

The complementary labyrinth is generated by mirroring the original. Then thus it looks:

The complementary Chartres labyrinth

The complementary Chartres labyrinth

The entry into the labyrinth happens on the 7th circuit, the center is reached from the 5th circuit. The barriers are differently arranged in the right and left axes, the upper ones remain. It is self-dual.

Without the barriers it looks thus:

The complementary Chartres labyrinth without the barriers

The complementary Chartres labyrinth without the barriers

The transformation again works, as it does for the original. The path sequence is: 7-8-9-10-11-6-1-2-3-4-5-12. Also this labyrinth is self-dual.

We confront it with the complementary labyrinth, generated from the seed pattern.

The complementary 11 circuit labyrinth made from the seed pattern

The complementary 11 circuit labyrinth made from the seed pattern

The path sequence on this is: 7-10-9-8-11-6-1-4-3-2-5-12.
Contrarily to the original this type did not show up historically.

So we have created two completely new 11 circuit labyrinths from the Chartres labyrinth, which look different than the 11 circuit labyrinths that can be developed from the seed pattern.

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How to make a Classical (Minoan) Labyrinth from a Medieval Labyrinth, Part 2

Quite simply: By leaving out the barriers in the minor axes. I have already tried this with the Chartres labyrinth (see related posts below). But is that also possible with any other Medieval labyrinth?

In part 1 I had made it for the type Auxerre. Now I take the type Reims which is also self-dual like Chartres and Auxerre. And again I take the complementary version. All examples are presented in the concentric style.

The Reims labyrinth

The Reims labyrinth

 

Here the original with all lines and the path in the labyrinth, Ariadne’s thread. The barriers in the upper minor axis are identical with those in the type Chartres, the barriers in the horizontal axis are different from Chartres, as well as the arrangement of the turning points in the main axis below the center.

The Reims labyrinth without the barriers

The Reims labyrinth without the barriers

The barriers are left out. When drawing the path I had to discover that four lanes cannot be included. These are the both outermost and the both innermost tracks (1, 2, 10, 11). Hence, I have anew numbered the circuits and there remain only 7 circuits instead of the original 11. However, this also means that by changing the Reims  Medieval labyrinth into a concentric Classical labyrinth through this method not an 11 circuit labyrinth is generated, but a 7 circuit.

The circular 7 circuit labyrinth

The circular 7 circuit labyrinth

This is an up to now hardly known and not so interesting labyrinth. Since one enters the labyrinth on the first circuit and arrives at the center from the last. The path sequence is very simple: 1-2-3-4-5-6-7-8, a simple serpentine pattern.


Now we turn to the complementary labyrinth:

The complementary Reims labyrinth

The complementary Reims labyrinth

The complementary labyrinth is generated by mirroring the original one. The upper barriers remain, right and left they run differently and in the main axis, the turning points shift. The entrance into the labyrinth changes to the middle (lane 9) and the entrance into the center is from further out (lane 3).

The complementary Reims labyrinth without the barriers

The complementary Reims labyrinth without the barriers

As with the original four lanes can not be inserted (1, 2, 10, 11). Hence, a 7 circuit labyrinth arises again. I have anew renumbered the lanes and have drawn the labyrinth anew.

Then thus it looks:

The circular 7 circuit labyrinth

The circular 7 circuit labyrinth

The labyrinth is entered on the 7th lane, the center is reached from the first lane. The path sequence is: 7-6-5-4-3-2-1-8. This labyrinth does not belong to the historically known labyrinths. However, it has already appeared in this blog (see related posts below).

The surprising fact is that again no 11 circuit Classical labyrinth could be generated through the transformation. Rather two 7 circuit labyrinths.

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How to make a Classical (Minoan) Labyrinth from a Medieval Labyrinth, Part 1

Quite simply: By leaving off the barriers in the minor axes. I have already tried this with the Chartres labyrinth (see related posts below). But is that also possible with every other Medieval labyrinth?

As an example I have chosen the type Auxerre that Andreas showed here recently. This labyrinth is self dual as are Chartres and Reims, therefore of special quality. And they all have a complementary version.

The Auxerre labyrinth

The Auxerre labyrinth

Here the original with all the lines and the path in the labyrinth, Ariadne’s thread. The barriers in the minor axes are identical with those of the Chartres type. There is only another arrangement of the turning points (the lanes 4, 5, 7, 8) in the middle of the main axis.

The original Auxerre labyrinth without the barriers

The original Auxerre labyrinth without the barriers

The barriers are omitted. When drawing Ariadne’s thread, I found that four tracks could not be inserted. Hence, I have anew numbered the circuits and there remain now 7 circuits instead of the original 11. However, this also means that by changing this Medieval labyrinth into a concentric Classical labyrinth through this method no 11 circuit labyrinth is generated, but a 7 circuit.

The 7 circuit circular Cretan labyrinth

The 7 circuit circular Cretan labyrinth

If one looks more exactly at it, one recognises the well-known path sequence: 3-2-1-4-7-6-5-8. We got a Cretan labyrinth in concentric style.


Now we turn to the complementary labyrinth:

The complementary Auxerre labyrinth

The complementary Auxerre labyrinth

The complementary labyrinth is generated by mirroring the original one. The upper barriers remain, right and left they run differently and in the main axis, the turning points shift. The entrance into the labyrinth changes to the middle (lane 9) and the entrance into the center is from further out (lane 3).

The complementary Auxerre labyrinth without the barriers

The complementary Auxerre labyrinth without the barriers

As with the original, four lanes can not be inserted (4, 5, 7, 8). Therefore, the result is again a 7 circuit labyrinth. I renumbered the lanes and have redrawn the labyrinth.

This is how it now looks like:

The complementary 7 circuit circular Cretan labyrinth

The complementary 7 circuit circular Cretan labyrinth

The labyrinth is entered on the 5th lane, the center is reached from the 3rd lane. The path sequence is: 5-6-7-4-1-2-3-8. This labyrinth is not one of the historically known labyrinths. But it showed up in this blog several times (see related posts below). Because it belongs to the interesting labyrinths among the mathematically possible 7 circuit labyrinths.

The surprising fact is that no 11 circuit Classical labyrinth could be generated through the transformation. But for that  the 7 circuit Cretan labyrinth. Therefore we can say that the heart of the Medieval Auxerre labyrinth is the Cretan (Minoan) labyrinth as it is in the Chartres labyrinth.

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Variations on the Babylonian Visceral Labyrinths in Knidos Style

By rotating or mirroring one will get dual and complementary labyrinths of existing labyrinths. Or differently expressed: Other, new labyrinths can be thereby be generated.
So I have three more new labyrinths as I can make a complementary one from a new dual labyrinth and I can make a dual one from a new complementary, which are identical. (For more see the Related Posts below).

Seen from this angle I have examined the still introduced 21 Babylonian Visceral Labyrinths in Knidos style and present here the variations most interesting for me. Since not each of the possible dual or complementary examples seems noteworthy.

Many, above all complementary ones, would begin on the first circuit and lead to the center on the last, which is yet undesirable.

Leaving out trivial circuits also will generate new labyrinths. This applies to the last two ones. If you compare the first and the last example you see two remarkable labyrinths: The first with 12 circuits and the last with 8 circuits, but using the same pattern.

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The Babylonian Visceral Labyrinths in Knidos Style

To say it more exactly, here I relate to the 21 row-shaped visceral labyrinths, still known from some of the previous articles (see Related Posts below).

The appearance is defined by the circuit or path sequence. With that one can construct the different and new labyrinth types (here 21). To this I use the once before presented method to draw a labyrinth (see below).

The path and the limitation lines are equally wide. The center is bigger. The last piece of the path leads vertically into the center. All elements are connected next to each other without sharp bends and geometrically correct. There are only straight lines and curves. This all on the smallest place possible. All together makes up the Knidos style.

Look at a single picture in a bigger version by clicking on it:

I think that by this style the movement pattern of every labyrinth becomes especially well recognizable. With that they can be compared more easy with the already known labyrinths.

Remarkably for me it is that only one specimen (E 3384 v_6) begins with the first circuit. And the fact that many directly circle around the middle and, finally, from the first circuit the center directly is reached. Noticeably are also the many vertical straight and parallel pieces in the middle section.

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How to Transform the Babylonian Visceral Labyrinths into One-Arm Alternating Labyrinths

Here it is about the decoding of the circuit sequences of the row-shaped 21 visceral labyrinths shown in the last article on this subject (see related posts below).

The question is: Can I generate one-arm alternating labyrinths with one center in the middle from them? That means no walk-through labyrinths where the also unequivocal path passes through, but is ending at an aim in the middle.
Maybe one could call them “walk-in labyrinths” contrary  to the “walk-through labyrinths”?

The short answer: Yes, it is possible. And the result are 21 new, up to now unknown labyrinths.

The circuit sequence for the walk-through labyrinth can be converted into one for a walk- in labyrinth by leaving out the last “0” which stands for “outside”. The highest number stands for the center. If it is not at the last place in the circuit sequence, one must add one more number.
This “trick” is necessary only for two labyrinths and then leads to labyrinths with even circuits (VAT 984_6 and VAN 9447_7).

The gallery shows all the 21 labyrinths in concentric style with a greater center.

Look at the single picture in a bigger version by clicking on it:

 

All labyrinths are different. Not one has appeared up to now somewhere. They have between 9 and 16 circuits, the most 11 circuits. They show between 3 and 6 turning points.

In these constellations there are purely mathematically seen 134871 variations of interesting labyrinths, as proves Tony Phillips, professor of mathematics.

There are still a lot of possibilities to find new labyrinths or to invent them.

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Further Link
The website of Tony Phillips

How would the Classical Labyrinths look as Babylonian Visceral Labyrinths?

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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