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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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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

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We hope you had a good start in new year. This year again promises intersting insights into the world of labyrinths.

 

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Or more precisely: The circuit sequence of the the row-shaped visceral labyrinths. Amongst the up to now known 27 visceral labyrinths there are 21 row-shaped visceral walk-through labyrinths.  The circuit sequence may serve as a distinguishing feature. Here I would like to show the sequences of all 21 specimens.

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

The method is to number the vertical loops in series from left to right. The shifting elements do not receive a number. Besides, “0” stands for outside. The transverse loops in E 3384 r_4 and E 3384 r_5 are numbered the same way. A special specimen is E 3384 v_4. Here some loops are “evacuated”. However, also there a useful circuit sequence can be found.

All labyrinths are different. No one is like the other. That alone is remarkable. So they do not follow an uniform pattern.

A first look at the circuit sequences shows that they resemble very much the circuit sequences of the one-arm alternating classical labyrinths. That means: The first digit after 0 is always an odd number. Then even and odd numbers are following alternating.

One of the next articles will deal with the decoding of the circuit sequences.

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

Christmas tree Labyrinth

The complementary 7 circuit Classical labyrinth as Christmas tree Labyrinth

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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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We take a 7-circuit classical labyrinth and number the single circuits from the outside inwards. “0” stands for the outside, “8” denotes the center. I take this two numbers into the circuit sequence, although they are no circuits. As start and end point they help to better understand the structure of the labyrinth.

Ariadne's thread in the 7-circuit labyrinth

Ariadne’s thread in the 7-circuit labyrinth

The circuit sequence is: 0-3-2-1-4-7-6-5-8

Everybody which already has “trampled” Ariadne’s thread (the path) in the snow knows this: Suddenly there is no more place in the middle, and one simply goes out. And already one has created a walk-through labyrinth. This is possible in nearly all labyrinths.

Then maybe it looks like this:

Ariadne's thread in a walk-through labyrinth

Ariadne’s thread in a walk-through labyrinth

If one wants a more compact labyrinth, one must change the shape. The internal circuits become, in the end, a double spiral. We can make either two separate ways or join them. So we will get a bifurcation.

Just about:

The 7-circuit walk-through labyrinth

The 7-circuit walk-through labyrinth

We will get the following circuit sequence if we take the left way or the fork to the left:
0-3-2-1-4-7-6-5-0

Now we take first the right way or the fork to the right, then the circuit sequence will be:
0-5-6-7-4-1-2-3-0

Because the two rows are written among each other, they simply can be add up together (without the first and the last digit):
8-8-8-8-8-8-8

This means: If I go to the left, I am in the original labyrinth, if I go to the right, I cross the complementary one.

The complementary labyrinth of the 7-circuit labyrinth

The complementary labyrinth of the 7-circuit labyrinth

It has the circuit sequence 0-5-6-7-4-1-2-3-8.

Or said in other terms: The walk-through labyrinth contains two different labyrinths, the original one and the complementary one.

The 7-circuit labyrinth is self-dual. Therefore I only get two different labyrinths through rotation and mirroring as Andreas has described in detail in his preceding posts.

How does the walk-through labyrinth look if I choose a non self-dual labyrinth?

I take this 9-circuit labyrinth as an example:

A 9-circuit labyrinth

A 9-circuit labyrinth

Here the boundary lines are shown.
On the top left we see the original labyrinth, on the right side is the dual to it.
On the bottom left we see the complementary to the original (on top), on the right side is the dual to it.
However, this dual one is also the complementary to the dual on top.

The first 9-circuit walk-through labyrinth

The first 9-circuit walk-through labyrinth

The first walk-through labyrinth shows the same way as in the original labyrinth if I go to the left. If I go to the right, surprisingly the way is the same as in the complementary labyrinth of the dual one.

And the second one?

The second 9-circuit walk-through labyrinth

The second 9-circuit walk-through labyrinth

The left way corresponds to the dual labyrinth of the original. The right way, however, to the complementary labyrinth of the original.

Now we look again at a self-dual labyrinth, an 11-circuit labyrinth which was developed from the enlarged seed pattern.

An 11-circuit labyrinth in Knidos style

An 11-circuit labyrinth in Knidos style

The left one is the original labyrinth with the circuit sequence:
0-5-2-3-4-1-6-11-8-9-10-7-12

The right one shows the complementary one with the circuit sequence:
0-7-10-9-8-11-6-1-4-3-2-5-12

The test by addition (without the first and the last digit):
12-12-12-12-12-12-12-12-12-12-12

Once more we construct the matching walk-through labyrinth:

The 11-circuit walk-through labyrinth

The 11-circuit walk-through labyrinth

Again we see the original and the complementary labyrinth combined in one figure. If we read the sequences of circuits forwards and backwards we also see that both labyrinths are mirror-symmetric. This also applies to the previous walk-through labyrinths.

Now this are of all labyrinth-theoretical considerations. However, has there been such a labyrinth already as a historical labyrinth? By now I never met a 7- or 9-circuit labyrinth, but already an 11-circuit walk-through labyrinth when I explored the Babylons on the Solovetsky Islands (see related posts below). Besides, I have also considered how these labyrinths have probably originated. Certainly not from the precalled theoretical considerations, but rather from a “mutation” of the 11-circuit Troy Towns in the Scandinavian countrys. And connected through that with another view of the labyrinth in this culture.

There is an especially beautiful specimen of a 15-circuit Troy Town under a lighthouse on the Swedish island Rödkallen in the Gulf of Bothnia.

A 15-circuit Troy Town on the island Rödkallen

A 15-circuit Troy Town on the island Rödkallen, photo courtesy of Swedish Lapland.com, © Göran Wallin

It has an open middle and the bifurcation for the choice of the way. This article by Göran Wallin on the website Swedish Lapland.com reports more on Swedish labyrinths.

For me quite a special quality appears in these labyrinths, even if there is joined a change of paradigm.

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