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Posts Tagged ‘circuit sequence’

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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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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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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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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