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A very beautiful labyrinth example (fig. 1) named Cakra-vyuh can be found in Kern’s Book° (fig. 631, p. 294).

Andere 5

Figure 1: Cakra-Vyuh Labyrinth from an Indian Book of Rituals

The figure originates from a contemporary Indian book of rituals. In this, a custom of unknown age, still in practice today, was described, in which the idea of a labyrinth is used to magically facilitate birth-giving. To Kern this is a modified Cretan type labyrinth. I attribute it to a type of it’s own and name it after Kern’s denomination type Cakra-Vyuh (see Related Posts: Type or Style / 14).

The seed pattern is clearly recognizable. One can well figure out that this labyrinth was constructed based on the seed pattern. Despite this, I hesitate to attribute it to the Classical style. For this, the calligraphic looking design deviates too much from the traditional Classical style. The walls delimiting the pathway all lie to a mayor extent, i.e. with about 3/4 of their circumference on a grid of concentric circles. Therefore it has also elements of the concentric style. The labyrinth even somewhat reminds me of the Knidos style with its seamlessly fitting segments of arcs where the walls delimiting the path deviate from the circles and connect to the seed pattern.

Therefore I have not attributed this labyrinth to any one of the known styles, but grouped it to other labyrinths (Type or Style /9). However, I had also drawn this labyrinth type in the Man-in-the-Maze style already (How to Draw a Man-in-the-Maze Labyrinth / 5).

SPCV

Figure 2: Composition of the Seed Pattern

Fig. 2 shows how the seed pattern is made-up. We begin with a central cross. Tho the arms of this cross are then attached half circles (2nd image). Next, four similar half circles are fitted into the remaining spaces in between. Thus the seed pattern includes now 8 half circles (3rd image). Finally, a bullet point is placed into the center of each half circle. We now have a seed pattern with 24 ends, that all lie on a circle.

In the pattern it can be clearly seen, that the labyrinth has an own course of the pathway. Therefore, to me it is a type of it’s own.

Typ Cakra Vyuh

Figure 3: Pattern

Furthermore it is a self-dual, even though, according to Tony Phillips, uninteresting labyrinth (Un- / interesting Labyrinths). This because it is made-up of a very interesting labyrinth with 9 circuits with one additional, trivial circuit on both, the inside and the outside.

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°Kern, Hermann. Through the Labyrinth – Designs and Meanings over 5000 Years. Munich: Prestel 2000.
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For this kind of labyrinth there is quite an easy basic pattern: Three dashes and two dots. Just as if it were written in our hand. That is what I say to the kindergarten children with whom I explore the labyrinth.

The seed pattern: 3 dashes, 2 dots

The seed pattern: 3 dashes, 2 dots

With it one can draw round or angular labyrinths, but also a square one.

curved

curved

circular

circular

angular

angular

An other nice exercise (not only) for children) is to lay a square labyrinth with matches, paper clips, drinking straws or similar objects similar in size. The center will be three units big, and with a total of 95 components one can make the labyrinth.

A square match labyrinth

A square match labyrinth

The two dots of the seed pattern are replaced by two elements placed horizontally: The left one below, the right one above the vertically arranged three objects.

The seed pattern

The seed pattern

Then we connect the elements with each other, as we already know it from the classical 7 circuit labyrinth. The distance between the lines corresponds to the length of an element.

Children want to trace the way in the labyrinth over and over again, even walk the path. This just succeeds for a width of 20 cm, however, the straws soon will get out of place.

Thus the desire arise to make something more firm. This can best be realized with adhesive tape on the floor. To get the labyrinth really square and rectangular, we need for that a method and a little scheme.

The drawing

The drawing

First we fix a base line. Then the third corner point should be defined. We intersect the diagonal and the side length of the square, outgoing from one end point of the base line. With the same technique the fourth corner point is build. The four sides of the square and both diagonals must have the correct length. So we have produced a figure at right angles.
Then best of all one fixes the end points of the inner lines with the help of the diagonals. After that one connects point for point and will get right-angled lines. The diagonal measurements should better be made by adults, the connection of the points could again be made by the children.

The drawing is designed as a prototype for a unit of 1 m. All specified dimensions are scaleable, so they can be used for labyrinths in different dimensions. For the above shown blue labyrinth all dimensions has been multiplied by the factor 0.21. This proves a path width of nearly 21 cm, an edge length of 1.89 m for the labyrinth, and a total of about 20 m for the lines (adhesive tape).

Here you may see, print, save or copy the PDF file of the drawing

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Summary

As is the case with the labyrinth itself and the seed pattern, there are also two representations of the rectangular form: this can be represented either with the walls or with the Ariadne’s Thread. In addition, there are two methods to obtain the rectangular form and therefore two versions of it. Ill. 1 summarizes this with the example of my demonstration labyrinth.

L:SP:P Rep

Illustration 1. Overview

This illustration shows on the first line the labyrinth (figures 1), on the second line the seed pattern (figures 2), on the third line the rectangular form obtained with method 1 (figures 3) and on the bottom line the rectangular form obtained with method 2 (figures 4). Each of these are shown in the representation with the walls (left figures a) and with the Ariadne’s Thread (right figures b).

  • When we speak of a „labyrinth“ we usually mean the labyrinth in its representation with the walls. This is shown in fig. 1 a. But also the representation with the Ariadne’s Thread is in widespread use and generally well known (fig. 1 b). This is usually simply referred to as the Ariadne’s Thread.
  • Fig. 2 a shows the seed pattern for the walls, fig. 2 b the seed pattern for the Ariadne’s Thread. As Erwin and I have written so much about this in recent posts, I don’t elaborate more on it here.
  • If we start from the labyrinth (fig. 1 a) or from the Ariadne’s Thread (fig. 1b) and apply method 1, we will as a result obtain the rectangular forms shown in line 3. Thus, there exists a rectangular form for the walls (fig. 3a) as well as for the Ariadne’s Thread (fig. 3b).
  • If we apply method 2 this results in the rectangular forms of line 4. These are the same as the figures on line 3, although rotated by half the arc of a circle.

For what I termed “rectangular form” here, in the literature we can find also the terms „compression diagram“ or „line diagram“ or else. And, most often, we will encounter rectangular forms for the walls obtained with method 1, i.e. figures like fig. 3 a.

RF BM M1

Illustration 2. Figure 3a

I, however, always use the rectangular form for the Ariadne’s Thread. This is the simpler graphical representation. Furthermore, I use the version obtained with method 2, as the result can be read from top left to bottom right, what corresponds better with the way we are used to read. This figure (e.g. fig. 4 b), the rectangular form for the Ariadne’s Thread obtained with method 2, is what I refer to as the pattern.

RF AF M2

Illustration 3. Figure 4b

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Method 1

In my last post I have shown how the seed pattern can be transformed into the pattern. The same result can be obtained by transforming the Ariadne’s Thread into the rectangular form.

Lage KS

Figure 1. Ariadne’s Thread and Situation of the Seed Pattern

Fig. 1 shows the Ariadne’s Thread of my demonstration labyrinth with the seed pattern highlighted. In addition the situation of the entrance (arrow) and of the center (bullet point) is indicated.

AF-M

Figure 2. Rotating the Right Half of the Axis…

In fig. 2 we now fix the left half of the axis and rotate the right half anticlockwise a full turn along the circuits. By this, the circuits are continually shortened. Immediately before the right half reaches the left half of the seed pattern on its opposite side, the circuits have reduced to very short lines. But, as can be seen, it is really the circuits of the labyrinth, that connect the ends of both halves of the seed pattern.

Mäander_Meth1

Figure 3. … Until it Meets the Left from the Other Side

At the point where both halves meet each other, these remaining pieces of the circuits disappear. In lieu of them the straight of the meander appears. This is composed of the outer vertical lines of the original auxiliary figure of the seed pattern.

Therefore, it is absolutely justified to straighten-out the meander at the point where it intersects with the vertical straight. The lines that connect the ends of the seed pattern really represent the circuits of the labyrinth.

In fig. 3 we have now generated the meander starting from the Ariadne’s Thread, fixing one half of the seed pattern and rotating the other by a full turn. I refer to this way of generating the pattern as method 1. I had fixed the left half and rotated the right half.

Muster Meth1b

Figure 4. Rotating the Left Half of the Axis by a Full Turn

Fig. 4 shows that we could also fix the right half and rotate the left. In the result, this makes no difference.

Muster Erg1

Figure 5. Result: Pattern with Entrance on Below Right and Center on Top Left

The result of this method is in both cases the same meander that is straightened-out to the pattern as described previously.

Important: Please notice, that after this transformation, in the pattern the entrance lies on the bottom right and the center on top left. This result is against our spontaneous intuition and also contradicts with how we are used to read. It is a result of the applied method 1.

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In several previous posts I have shown, that different variants can exist for a certain labyrinth or seed pattern.

KSAF_var

Illustration 1. Variants of the Same Seed Pattern

In Ill. 1 I again show some variants of the seed pattern for the Ariadne’s Thread of my demonstration labyrinth. This same seed pattern can be drawn e.g. with a circular, elliptic, petal-shaped or rectangular outline. The outline figure is only an auxiliary figure. The seed pattern itself is formed by the system of lines within this outline figure. Depending on the shape of the outline figure, also the orientation and rounding of the seeds may somewhat differ. However, they are always ordered the same way. On top left one (not-nested) turn, on bottom left two nested and on the right three nested turns. Which variant of the seed pattern is best suited depends on the purpose for which it is used.

In this post I want to show the relationship between the seed pattern and the pattern. For this purpose, the rectangular variant is best suited. The seed pattern can be transformed to the pattern in a few steps.

KS Umf1

Illustration 2. From Seed Pattern to Meander

The left figure of ill. 2 shows the rectangular variant of the seed pattern. This is also shown as baseline in grey in the right figure. As a first step, the right half of the seed pattern is shifted against the left (shown in red), until it comes to lie on the other side of the left half.

KS Umf2

Illustration 3. From Meander to Pattern

The result of this shift is a meander. It is one of Arnol’d’s figures. This meander is in a next step straightened-out, as has already been shown here. For this, the right half of the seed pattern is shifted somewhat further to the left. The ends opposite each other are then connected with lines.

KS Muster

Illustration 4. Pattern

The result of this process is shown in ill. 4. Apparently, in transforming the meander to the pattern, the first and most important step is the horizontal straightening-out. By this the situation of the circuits in the pattern are made apparent. Next, one can easily straighten-out the axial segments and finalize the pattern.

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In my last post I have shown that a seed pattern can also be drawn in labyrinths with multiple arms (see related posts). With the seed pattern for the Ariadne’s Thread it is possible to connect the arms in the shape of a flower (or a propeller). For each arm, a separate petal is needed.

Figure 1. Borderlines

Figure 1. Borderlines

These auxiliary figures can all be drawn in one continous  line.

Figure 2. How to Draw the Borderline

Figure 2. How to Draw the Borderline

Fig. 2 illustrates this with a three-arm labyrinth. Other flowers with multiple arms can be drawn the same way.

Each of the petals contains a part-seed pattern. I will show this using an example of one of my five-arm labyrinth designs. I choose the design KS 2-3 that has been installed as a temporary labyrinth on the square of Magdeburg cathedral. This labyrinth can be actually seen in the header of this blog. Otherwise there is an image of it here.

Figure 3. KS 2-3

Figure 3. KS 2-3

Fig. 3 shows the labyrinth in a drawing by Erwin of the walls and with the Ariadne’s Thread (red) inscribed.

Figure 4. Seed Pattern for the Ariadne's Thread

Figure 4. Seed Pattern for the Ariadne’s Thread

In fig. 4 the seed pattern for the Ariadne’s Thread is shown per se and completed to the whole Ariadne’s Thread. In order to complete this seed pattern, for each circuit 10 ends have to be connected with five segments of a circuit. Evidently, with an increasing number of arms, the seed pattern comes to look closer to the entire labyrinth. The part-circuits are shortened in relation to the part-seed patterns.

The seed pattern has first and most often been published for the walls of the Cretan type labyrinth. Also for several other one-arm labyrinths, seed patterns have been published. Therefore, the seed pattern does not constitute a characteristic attribute of the Cretan type labyrinth. It is not even a characteristic specific for one-arm labyrinths alone.

However, the use of seed patterns in labyrinths with multiple arms is of minor practical importance. The original purpose and meaning of the seed pattern was, that it enables us to capture the essential of a labyrinth with a simple memorable system of lines that allows us to generate the labyrinth straight away. And this applies best to the seed patterns of the Cretan type labyrinth and its relatives of the vertical line.

Figure 5. Seed Patterns of the Cretan Labyrinth and it's Relatives of the Vertical Line

Figure 5. Seed Patterns of the Cretan Labyrinth and it’s Relatives of the Vertical Line

Fig. 5 shows the seed patterns for the walls in the first column and for the Ariadne’s Thread in the second column. The corresponding types of labyrinths are on

  • row 1: Löwenstein 3
  • row 2: The Cretan
  • row 3: Hesselager
  • row 4: Tibble

 

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The seed pattern is an extract of the axis of the labyrinth without the circuits. A seed pattern can also be drawn for labyrinths with multiple arms.

Figure 1. The Arms

Figure 1. The Arms

Fig. 1 shows this with a one-arm and a two-arm labyrinth compared. The one-arm labyrinth is of the Cretan type, the two-arm labyrinth is one of my own designs. For reasons of simplicity I chose the representation with the Ariadne’s Thread.

In labyrinths with multiple arms a separate seed pattern has to be extracted for each arm. Of course, these two parts belong together. This should become directly evident.

The seed pattern for the Ariadne’s Thread is drawn with an auxiliary line that delimits the layout of the seed pattern (see related posts below). This auxiliary line can be used to graphically connect the two part-seed patterns.

Figure 2. Connecting the Part-Seed Patterns

Figure 2. Connecting the Part-Seed Patterns

Figure 2 shows how we can prodeed for this. In one-arm labyrinths the center lies beyond the seed pattern. And, strictly speaking, it always has to be indicated, where the center of the labyrinth is situated. In labyrinths with two arms the seed pattern of the side-arm is situated beyond the center opposite to the seed pattern of the main axis of the labyrinth. In a seed pattern of a labyrinth with multiple arms, the center is fixed by the situation of the arms relative to each other. And thus it comes to lie within the seed pattern. With the auxiliary line the sub seed patterns for the Ariadne’s Thread can easily be connected in the shape of an “8”. This can be drawn freehand in one line. By doing so, we have performed a variation of the original circular or elliptic form to a petal-shaped form. This, however, is a minor variation and does not affect the seed pattern itself.

Figure 3. Completing the Seed Pattern for the Ariadne's Thread

Figure 3. Completing the Seed Pattern for the Ariadne’s Thread

As fig. 3 shows, the seed pattern of a multi-arm labyrinth is completed exactly the same way as a one-arm labyrinth seed pattern (see related posts). The ends of the seeds nearest to the centre are connected first. By this, the innermost circuit is generated. Next, the ends nearest to the first circuit are connected the same way, and so forth. And so, one circuit after another is added from the inside out. The only difference to a one-arm labyrinth is, that in a multiple-arm labyrinth multiple segments have to be generated for each circuit. In a two-arm seed pattern, for each circuit, four ends have to be connected with two sections of circuits between the two arms.

There are two notable differences in the shape of the seed pattern of the main axis and of the side arms.

  • The seed pattern of the main axis has two ends more than the seed patterns for the side arms. This is due to the fact that the entrance of the labyrinth and the access to the center lie on the main axis.
  • Usually we consider alternating labyrinths where the path does not traverse the main axis (although there are some notable exceptions). In these labyrinths it is indispensable that the path traverses the side arms. Otherwise it would not be possible to reach the area opposite the side-arm and it thus would be impossible to generate the side arm at all.
Figure 4. Completing the Seed Pattern for the Walls

Figure 4. Completing the Seed Pattern for the Walls

Of course, what is valid for the Ariadne’s Thread works with the walls of the labyrinth too. The seed pattern for the walls, however, looks more complicated and less elegant. The part-seed patterns of the two arms are not graphically connected, as the seed pattern for the walls traditionally is drawn without an auxiliary line. The Ariadne’s Thread is the simpler graphical representation of both, the labyrinth and the seed pattern of it.

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