Feeds:
Posts
Comments

Posts Tagged ‘Type Knossos’

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.

Related Posts

Read Full Post »

The Spokes of the Auxiliary Figure

In all earlier posts on this subject I have considered labyrinths with 7 circuits. The auxiliary figures of these labyrinths all have 16 spokes. The number of spokes of the auxiliary figure is determined by the number of the ends of the seed pattern. I will show this here for some selected labyrinths with less or more than 7 circuits. The first two examples are the only alternating labyrinths with three circuits. The third is a labyrinth with 11 circuits.

Type Löwenstein 3

Type Löwenstein 3

The simpler labyrinth with three circuits is of the Löwenstein 3-type. The seed pattern of this labyrinth has 8 ends. The pattern is made-up of a serpentine from the outside in. This labyrinth again contains the smallest possible seed pattern that covers only one circuit in the MiM auxiliary figure. Therefore the auxiliary figure has 8 spokes and consists of three circuits for the labyrinth, one for the center and one more for the seed pattern. For the boundaries of the five circuits, six rings are needed.

Type Knossos

Type Knossos

The other is the well-known Knossos-type labyrinth. The auxiliary figure for this type of labyinth has also 8 spokes. The pattern of this labyrinth, however, is made-up of a single double-spiral like meander (Erwin’s type 4 meander). This has two nested turns on each half of the seed pattern. It is this the largest possible seed pattern for a labyrinth with three circuits in the MiM-style. The seed pattern covers two circuits. Therefore, the auxiliary figure for this labyrinth needs 6 circuits / 7 rings, which is one more than the Löwenstein-type labyrinth.

As a third example I show the Otfrid-type labyrinth in the MiM-style.

Type Otfrid

Type Otfrid

Ths seed pattern of this type of labyrinth has 24 ends as is the case with all other labyrinths with 11 circuits. Thus, the auxiliary figure has 24 spokes. In addition the seed pattern consitsts of six similar sixth parts, each of which is made-up of two nested turns. It therefore covers two circuits. The auxiliary figure thus has 11 circuits for the labyrinth plus one for the center and two for the seed pattern, in all 14 circuits and 15 rings.

Seed Patterns with Single (Erwin's Type 4) Meanders

Seed Patterns with Single (Erwin’s Type 4) Meanders

The seed patterns of the Knossos-, Cretan- and Otfrid-type labyrinths all need two circuits in the MiM auxiliary figure. Remember that the Knossos type labyrinth is made-up of one, the Cretan of two and the Otfrid-type labyrinth of three single double-spiral-like (Erwin’s type 4) meanders. These are the three labyrinths of the horizontal line of the labyrinths directly related with the Cretan labyrinth.

Related posts:

Read Full Post »

Erwin has demonstrated  that it is possible to inscribe the Ariadne’s Thread of the Knossos-type labyrinth into the Flower of Life. For this, a pathway has to be followed along the lentiform segments in the appropriate manner (figure 1).

Figure 1: Type Knossos

Figure 1: Type Knossos

These lentiform segments form a grid of overlapping hexagons. This grid is generated solely by arranging a number of circles with the same size so that they intersect each other accordingly. The Flower of Live covers an area with a diameter of three such circles. This corresponds with the number of circuits a labyrinth can have to be inscribed into the Flower of Life.

Figure 2: 3 circles = 3 circuits

Figure 2: 3 circles = 3 circuits

Figure 2 shows the reason. Three concentric hexagons can be arranged around the center of the Flower of Life. The circuits of the labyrinth lie on these hexagons. Only the axis remains to be designed in the right way. For this, the closed circuits have to be interrupted and connected with other circuits.

It is therefore also possible to inscribe the other well known labyrinth with three circuits, the Löwenstein 3 – type labyrinth, into the Flower of Life (figure 3).

Figure 3: Type Löwenstein 3

Figure 3: Type Löwenstein 3

Larger labyrinths, however, cannot be inscribed into the Flower of Life in the same way. They need a bigger area covered with the hexagonal grid. For a labyrinth with seven circuits, e.g. the “Cretan”-type Labyrinth, an area with a diameter of seven circles is required, as shown in figure 4. I leave it to the reader to inscribe the Ariadne’s Thread of the labyrinth (beginning at the arrow / end at the bullet point).

Please note:  You may copy and print the figure by a right mouse click to draw Ariadne’s Thread easier. 

Figure 4: Flower of Life for 7 circuits

Figure 4: Flower of Life for 7 circuits

Related Posts:

Read Full Post »

There are two important lines in a labyrinth:

  • The one is the so-called Thread of Ariadne, the path or way from the entrance into the middle and back again. This is always an uninterrupted line, without branches or overlaps.
  • These are the boundary lines (the walls, the sidelines) which delimitate the way, and between those the way runs. They may cross already once and overlap.

Only one of both lines is mostly shown in a labyrinth. Frequently this are the boundary lines. For a labyrinth that can be walked this is so almost always. Then the way is the free space between these lines.
However, in drawings or images even only the thread or even both can be shown.
This can be sometimes confusing if one has to distinguish a labyrinth from a maze.

The whole labyrinth inside the flower of life

The whole labyrinth inside the flower of life

In my first article (see Related Post below) I had only marked the way (Ariadne’s thread) that is contained within the flower of  life. It is the path of a 3 circuit labyrinth from the type Knossos with the path sequence 3-2-1-4.
The corresponding boundary lines arise if one constructs other lines parallel to the path. These also run between all petals, only the extreme line runs outside, however, touches the outside circle of the flower of life at six spots and thereby forms a hexagon, a honeycomb.
In this labyrinth even the walls form only one single line. They run from one turning point to the other one without crossing each other.
The cube enclosed in the flower of life is even very good to recognize.

The labyrinth unites square and circle. And here still the hexagon as a basic element of life for growth and development.

Related Post

Read Full Post »

I had to take over this task recently. There was a birthday party and there was short of space.
On this occasion a 3 circuit labyrinth fits best. Nevertheless, it is good to have enough width for the path to walk. And a bigger middle. Thus I adopted a circular labyrinth with the path sequence 0-3-2-1-4.

A 3 circuit Knidos labyrinth

A 3 circuit Knidos labyrinth

I had a space of about 4 m. As path width I chose 50 cm, the middle had a diameter of 1 m, and the overall diameter was 4 m. Thus arose a length of about 39 m for the walls which can be marked, e.g., very well with a rope. I have done this with two ropes of 20 m length.

The 3 circuit labyrinth

The 3 circuit labyrinth

The 3 circuit labyrinth

The 3 circuit labyrinth

But I was not really pleased with it. Since the middle seemed to me a little bit too small. I still hold the 4-fold path width as a good measure for the center.
Hence, I have developed a sort of prototype which I would like to introduce here:

A 3 circuit Knidos labyrinth with a dimension between axes of 1 m

A 3 circuit Knidos labyrinth with a dimension between axes of 1 m

The dimension between axes is 1 m, the center has 4 m and the overall diameter is 10 m. The walls have a length of 86.83 m, the way into the center amounts to 66.34 m. The other dimensions and the radii can be taken from the drawing.

One can split the whole distance of the walls: So I get 38.56 m from A to C, and 48.27 m from B to C (total length 86.83 m). This can be laid, e.g., with two ropes of 50 m and 40 m length.

The walls do not overlap and are made from one line, differently to the 7 circuit classical labyrinth.

Here you may see, copy or print the design drawing as a PDF file.


The whole is scaleable. That means that if you wish other widths or diameters, the radii, lengths (short all dimensions) will change accordingly. If, e.g., only a 4 m overall diameter is possible, the dimension between axes would become 40 cm and the internal radius 0.80 m (the center therefore 1.60 m). I must multiply all dimensions by the factor 0.4. The path length would be 26.54 m and the (splitted) walls 15.42 m and 19.31 m.


Here the dimensions of the prototype are multiplied by the factor 0.5. Everything becomes half as big: The dimension between axes 50 cm, the center 2 m and the overall diameter 5 m. The path length decreases to 33.17 m and the /splitted) walls are 19.28 m and 24.13 m (43.42 m added together).

A 3 circuit Knidos labyrinth with a dimension between axes of 50 cm

A 3 circuit Knidos labyrinth with a dimension between axes of 50 cm

Here too, you may see, copy or print the design drawing as a PDF file.

Related Post

Read Full Post »

The Dutch Maze and Labyrinth Symposium 2011 was in Eibergen, not far away from the labyrinth built in 2003 by the Scottish land artist Jim Buchanan. He used the square labyrinth design known from a Cretan coin, dated 430 – 350 B.C.

Classical square labyrinth with 3 circuits

Classical square labyrinth with 3 circuits

The artwork is at the place of the former castle of Mallem from which only the moat remained. In these historical surroundings Jim Buchanan has created the labyrinth by commission of the Rouffaer-van Heek Foundation as earthwork. The plateau covers 35 x 35 m with three right-angled circuits leading to a small circular tower in the centre. The rotunda is half in the earth, but open to the sky. The earth walls are about 1.50 m high, the pathways length amounts to 270 m.

Jim Buchanan was one of the expert speakers at the symposium. At the end of the first day there was a walk to the labyrinth with a special event. He had transformed the small rotunda into a camera obscura.

Here some impressions from the event:

Picture 1

Picture 1

Picture 2

Picture 2

Picture 3

Picture 3

Picture 4

Picture 4

Picture 5

Picture 5

Picture 6

Picture 6

Picture 7

Picture 7

Picture 8

Picture 8

Picture 9

Picture 9

.
One can perceive the labyrinth very good in Google Earth:

Read Full Post »

%d bloggers like this: