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When I dealt with the Knossos labyrinth it has struck me that the seed pattern can be simplified very easily. It can be reduced to three lines and two dots. To draw the labyrinth they are connected just as we do it for the classical labyrinth. For more information please see the Related Posts below.

Now this seed pattern with the two turning points can be extended in a very simple way, just by adding more lines in pairs.
seed pattern

The bigger labyrinths have more circuits, however, maintain her basic structure. And, nevertheless, these are own types, because they have another path sequence than the 7-, 9-, 11-, 15- etc. circuit  classical labyrinths. But they are not known, neither among the historical, nor among the contemporary labyrinths. Because they are too easy? Besides, the lines have quite a special rhythm. A closer look can be worthwhile.
The 3 circuit labyrinth of this type first appeared about 400 B.C. on the silver coins of Knossos:

The Labyrinth Type Knossos

The Labyrinth Type Knossos

The circuits are numbered from the outside inwards from 1 to 3. The center is marked with 4. The blue digits labels the circuits inside out. The path sequence is 3-2-1-4, no matter which direction you take. Through that a special quality of this labyrinth is also indicated: It is self-dual.

What now shall be the special rhythm? To explain this, we look at a 5 circuit labyrinth of this type:

The 5 circuit Knossos Labyrinth in the Cretan Style

The 5 circuit Knossos Labyrinth in the Cretan Style

The path sequence is: 5-2-3-4-1-6. At first I circle around the center (6) on taking circuit 5. Then I go outwardly to round 2, from there via the circuits 3 and 4 again in direction to the center, at last make a jump completely outwards to circuit 1, from which I finally reach the center in 6.


Here a 7 circuit labyrinth in Knidos style:

7 circuit Labyrinth in Knidos style

7 circuit Labyrinth in Knidos style

The path sequence is: 7-2-5-4-3-6-1-8. It is also self-dual. The typical rhythm is maintained, the “steps” are wider: From 0 to 7, from 7 to 2, and finally from 1 to 8 (the center).

Here a 9 circuit labyrinth in circular style:

9 circuit Labyrinth in circular style

9 circuit Labyrinth in circular style

The path sequence is: 9-2-7-4-5-6-3-8-1-10. The step size is anew growing. This labyrinth is self-dual again.

This example exists as a real labyrinth since the year 2010 on a meadow at Ostheim vor der Rhön (Germany):

9 circuit Labyrinth in circular style at Ostheim vor der Rhön (Germany)

9 circuit Labyrinth in circular style at Ostheim vor der Rhön (Germany)

To finish we look at a 11 circuit labyrinth in square style:

11 circuit Labyrinth in square style

11 circuit Labyrinth in square style

The path sequence is: 11-2-9-4-7-6-5-8-3-10-1-12. And again self-dual.

I think, the method is clear: We add two more lines more and we will get two circuits more. So we could continue infinitely.
The shape of the labyrinth can be quite different, this makes up the style. The path sequence shows the type. And for that kind of labyrinth we always have only two turning points.

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My Best Wishes for 2017

To all readers I wish a happy new year and many inspiring experiences with the labyrinth.

ks-3333-gf_12eck

This labyrinth exists since 2014. I still have written about a visit of the health garden containing it in my personal Blog (see Further Link below). Today we will look at the labyrinth itself.

Thus is the plan:

The Roman labyrinth

The Roman labyrinth

It is a serpentine-type Roman labyrinth with four sectors. The whole diameter amounts to 15 m, the middle has a diameter of 1.40 m. The ways are 40 cm wide and paved with granite stones. They are separated of each other by a 50-cm-wide grass verge. The whole way through the 7 circuits in the 4 sectors to the center amounts to about 182 m. The entrance of the labyrinth lies on the right beside the main axis. The dividing stripes of the single quadrants lie on a cross.

Some photographic impressions:

There are two videos on YouTube, here the first one:

And here the second:

In the meantime, I have considered what one could have made better in a “labyrinth-technically” way. Since the idea in itself of a Roman labyrinth in the middle of the health garden seems not to be so good realized.

The last piece of the path arriving the center should always lie on the central main axis. If one makes the middle a little bigger, one receives above all longer and steadier path segments around the middle. If one wants to reach this and maintain the whole diameter of 15 m, one can make the paths and the dividing stripes each 40 cm broad. Then the center would have a diameter of 3.2 m.
One could have built a better Labyrinth at the same place and with the same costs.

Here the layout drawing:

The layout drawing

The layout drawing

Related Post

Further Link (in German)

Christmas 2016

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

Classical 7 Circuit Christmas Tree Labyrinth

Classical 7 Circuit Christmas Tree Labyrinth

Circuits and Segments

In my last post I have shown the sequence of segments in labyrinths with multiple arms. This is unambigous. But as a disadvantage it does not indicate directly which circuit is encountered by the pathway.

Now it is also possible to keep the partition in segments but only number the circuits. This allows to indicate directly in the sequence of segments, which circuit is visited by the pathway. Thus the same number may repeatedly occur in this sequence. This works well in many cases but may also leed to problems. In the labyrinth I had shown in my last post the problem does not occur. Therefore I will illustrate it here with an other example. For this I chose the labyrinth by Valturius as this is a small, understandable example (Fig. 1).

valturius

Figure 1. Labyrinth by Valturius. Source: Kern 2000, fig. 315, p. 179.

This labyrinth from a military manuscript by Robertus Valturius of the 15th century has three arms and four circuits. (Please note, that the arms are not proportionally distributed. This, however, has no influence here. I therefore use a proportional distribution for reasons of simplicity.)

num_valturius

Figure 2. Numbering of the Segmente: Left Image by Segment, Right Image by Circuit

Figure 2 shows in the left image the partition and numbering by segments I had already used in my last post. The right Image shows the same partition of segments although numbered by circuits only. As the labyrinth has four circuits, there are 12 segments.

The labyrinth by Valturius is alternating. However there exists a non-alternating labyrinth with the same level sequence. And this brings us back to the problem.

sf_valturius

Figure 3. Sequences of Segments Numbered by Segments

Figure 3 shows the alternating labyrinth by Valturius (left image) and the non-alternating variation (right image). They show two different courses of the pathway. These are also correctly represented by the two different sequences of segments. Both sequences of segments are similar for the first 9 segments: 1 4 7 8 5 2 3 6 9 … The sequences of the three last segments, however, are different. In the labyrinth by Valturius the sequence continues with segments ……… 12 11 10. On the other hand, the sequence of segments in the non-alternating variation is ……… 10 11 12.

If, however, we number the segments by circuits, we lose the uniqueness.

uf_valturius

Figure 4. Sequences of Segments Numbered by Circuits

Figure 4 shows the same labyrinths as fig. 3. But with their segments numbered by circuits. Both variants have the same sequence of segments 1 2 3 3 2 1 1 2 3 4 4 4. So here we can always identify in the sequence of segments, which circuit is encountered by the pathway. However, for the same sequence of segments there may exist multiple (in this case two) different courses of the pathway. The same problem occured already in the level sequence of one-arm labyrinths.

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There is now a new labyrinth at this extraordinary and historically significant place.

In the church Mariä Schutz a labyrinth was built during the three-year period of renovation and rebuilding on the area of the Vogelsburg.
Father Bernhard Stühler, hospital chaplain of the Juliusspital, initiated it. Architect Stephan Tittl from the office SequenzSieben Würzburg made the architectural design of the church and delivered the layout. During the inauguration of the project turned out, that Sr. Hedwig Mayer, prioress of the Augustinusschwestern on the Vogelsburg, always had wished a labyrinth.

The new labyrinth

The new labyrinth

It’s a newly created sector labyrinth with 5 circuits. In the middle is a bowl-shaped pitch circle to divert the direction. The dividing bars form a cross and are arranged symmetrically.
The diameter amounts to 6 m, the middle to 2 m. The ways are 34 cm wide and are marked by a 6 cm wide brass sheet on the terrazzo floor. The way into the center amounts to about 64 m.

One enters the church from the south over an outside stair. On the left hand of the entrance is the labyrinth which is aligned to the west and the east. You enter it from the west, arriving the center, one looks to the east in the direction of the altar and leaves it also again in this direction.

The Oberpflegeamtsdirektor (Chief Administrative Officer) Walter Herbert of the Juliusspitalstiftung (foundation Juliusspital) said on occasion of the inauguration of the altar in May, 2016 to the interior design of the church:

With the elected interior design and with the labyrinth in the ground we would like to offer to every visitor of the Vogelsburg the possibility to find the way to one’s own center, to get back to basics and to find the possibility of steering towards God in the church space.

The segments of the 5 circuits

The segments of the 5 circuits

As Andreas proposed in his last article we can number the 20 segments for the 5 circuits in this 4-armed labyrinth. The sequence of segments can be derived from it for the pathways. Some segments form a connected section which runs through several quadrants. These segments can be marked by brackets. The sequence of segments then looks as follow: 9-5-(1-2-3-4)-8-12-(16-15)-11-(7-6)-10-(14-13) – (17-18-19-20)-21. I write the result a little bit differently than Andreas and still add the center at the end. Inside this labyrinth we have as a specific feature two segments which enclose the full length of a circuit.

Related Post

Further Links (in German)

In one-arm labyrinths, each circuit is represented by one number. Therefore it is possible to capture even quite large labyrinths appropriately with the level sequence. In labyrinths with multiple arms, the pathway may repeatedly encounter the same circuit. Various possibilities exist to take account of this in the level sequence. For this, according to the number of arms, the circuits have to be further partitioned to segments. Here I will show a method in which all segments are numbered through.

For this I use an example of a labyrinth that has repeatedly been presented on this blog. It has 3 arms and 3 circuits.

3_gaengig_3_achsig_rund

First, each circuit is partitioned to three segments. One segment corresponds with a unit of the pathway between two arms. Next, the segments have to be numbered through. This can be done in different ways. Here I number them from the outside to the inside and one circuit after each other.

segmente

Now we can track the course of the pathway through the various segments. This results in the sequence of segments encountered by the pathway. In labyrinths with multiple arms the level sequence thus extends to a sequence of segments.

The sequence of segments of this labyrinth is 7 4 1 2 5 8 9 6 3. The length of this sequence of numbers is a result of the number of circuits multiplied with the number of arms. Thus, for a labyrinth with 3 circuits and 3 arms, 9 numbers are required. Whereas in a one-arm labyrinth with 3 circuits only 3 numbers are needed.

However, besides the numbers no other information is needed. The sequence of segments itself determines where the pathway makes a turn or traverses an axis. In one-arm labyrinths this had to be indicated additionally by use of separators.

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