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Posts Tagged ‘Ariadne’s Thread’

I have already seen many pictures of finger labyrinths on the internet. Mostly they are made of wood or ceramics. They show the way in the labyrinth, Ariadne’s thread.
I do not like many of them. Especially the last part of the way, the entrance to the center, is often not so satisfactory. This is not very clear in some finger labyrinths; the path often runs from the side rather than from the bottom and perpendicular to the center.

That’s why I would like to present some own ideas on that.
In the classical 7 circuit labyrinth, the center is usually only as wide as the path itself and therefore less accentuated. That’s why I prefer to choose a slightly larger center, as we have it in the Knidos style. But not four times the axle width, but only the double.

That’s how it looks:

Ariadne's thread in Knidos style

Ariadne’s thread in Knidos style

The turning points are slightly shifted, the center is slightly enlarged. As a result, the last piece of the path runs perpendicular to the center.


In addition, the classical 7 circuit labyrinth can be centered very well. Since the first and the last part of the path are on the 3rd and 5th ambulatory.

That’s how it looks:

Ariadne's thread centered for a finger labyrinth

Ariadne’s thread centered for a finger labyrinth

The four turning points are shifted a bit more.
The empty space in the interior also is a bit more distorted.


Below is a kind of preview drawing for a round labyrinth of 33 cm diameter with all construction elements.

However, the dimensions are very well scalable. That is, for a smaller labyrinth, I use a corresponding scaling factor, which multiplies all measures.

For example, if I want it to be half the size, I multiply all measurements by 0.5.

If I want to reach a certain size, I determine the required scaling factor by dividing this size by 33 cm.

For a desired diameter of 21 cm, e.g. I calculate the scaling factor as follows: 21 cm : 33 cm = 0.636. I then multiply all the measurements with 0.636.

To convert the cm to inches, I divide by 2.54: The diameter becomes 33 : 2.54 = 13 inches.

Note for my inch-using visitors: Simply replace the measure unit “cm” by “inch” in the drawing and then calculate the desired size of your labyrinth as described above.

Design drawing

Design drawing

Here you might see, print or download it as a PDF file

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My co-author Andreas Frei reported in his last article about the labyrinth drawing rejected by Sigmund Gossembrot on folio 53 v. And thereby made the amazing discovery that in it principles of design have been applied to which so far not one known historical labyrinth was developed.
Not for the sector labyrinths of the Roman labyrinths or the various Medieval ones. Even among the contemporary labyrinths (for example, the London Underground’s 266 new types by Mark Wallinger), this new type does not show up.

However, the labyrinth derived by Andreas Frei has some extraordinary features that I would like to describe here in more detail.
First of all see a representation of the new type in concentric style:

The 7 circuit labyrinth of folio 53 v in concentric style

The 7 circuit labyrinth of folio 53 v in concentric style

Contained is the classic 7 circuit labyrinth, as it can be developed from the basic pattern. In the upper area and in the two side parts 3 barriers are inserted, which run over 4 courses and again create 6 new turning points. These barriers are arranged very evenly, they form an isosceles cross. This significantly changes the layout.

The entrance to the labyrinth is on lane 3, then in the 1st quadrant on the lower left side you immediately go to the lanes 6, 5, 4 and 7. Thereby the center is completely encircled (in all 4 quadrants).
In the 4th quadrant on the bottom right, you go back over the lanes 6, 3, 2 through the remaining quadrants to the 1st quadrant.
From here, you go around the whole labyrinth, in the 4th quadrant, you quickly reach the center via the lanes 4 and 5.
Twice the entrance is touched very closely: at the transition from lane 2 to 1 in the 1st quadrant and at the transition from lane 1 to 4 in the 4th quadrant.

Fascinating are also the two whole “orbits” in lanes 7 and 1. The two semicircles in lane 2 are remarkable too. Lanes 3, 4 and 5 are only circled in quarter circles.

All this results in a unique rhythm in the route, which appears very dynamic and yet balanced.

Of course, this is hard to understand on screen or in the drawing alone. Therefore, it would be very desirable to be able to walk such a labyrinth in real life.

So far there is no such labyrinth. Who makes the beginning?

The centered labyrinth of folio 53 v

The centered labyrinth of folio 53 v

This type can also be centered very well. This means that the input axis and the entrance axis can be centrally placed on a common central axis. This results in a small open area, which is also referred to as the heart space.

Also in Knidos style, this type can be implemented nicely. This makes it even more compact. However, the input axis is slightly shifted to the left, as it is also the case in the original.
Here the way, Ariadne’s thread has the same width everywhere.

The labyrinth of folio 53 v in Knidos style

The labyrinth of folio 53 v in Knidos style

And here, as a suggestion to build such a labyrinth, the design drawing for a prototype with 1 m axle jumps. The smallest radius is 0.5 m, the next one is 1 m larger.
With a total of 11 centers, the different sectors with different radii can be constructed.

The design drawing

The design drawing

The total diameter is depending on the width of the path at about 18 m, the path length would be 225 m.

As the axes of the path are dimensioned, Ariadne’s thread is constructed.
All dimensions are scalable. This means that the labyrinth easily can be enlarged or reduced.

And here you may download or print the drawing as a PDF file.

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In the context of the theme Labyrinth and Flower of Life, the similarity to a cube has been mentioned more often. The hexagonal shape of the labyrinth was just too reminiscent of a cube. And that got me looking for the labyrinth on the cube.

I have a magic cube and as a small brain training I solve it once a day. This is now memorized and routinely.

In Further Link below you can find out what a magic cube is.

First, I tried to put Ariadne’s thread on the small squares. This is relatively easy.

For better representation, the 6 sides of a cube are “flattened”:

The layout

The layout

You can draw in there Ariadne’s thread for a 3 circuit labyrinth type Knossos. Generally known, this has the path sequence: 3-2-1-4.
The beginning is on the frontside below at left. Then we go to the third line, to the second and the first line and finally to the center in 4 up in the middle square.

Ariadne's thread

Ariadne’s thread

And here in an isometric view:

Three views

Three views

I hope you can imagine that on the drawings?
We see the lines on 5 sides of the cube, the bottom remains empty. The middle is slightly larger, but we do not touch all the small squares.

Ariadne’s thread for the template with slightly thicker lines:

Ariadne's thread

Ariadne’s thread

If you want, you can download, print or copy the template as a PDF file.

Such a cube would certainly be quite easy to solve as a magic cube. Especially if you have a template of it in mind.

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Further Links

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Almost seven years ago, the flower of life was a topic in this blog. Now I would like to add a few things.
First, the original drawing of Ariadne’s thread in the flower of life. During a visit to Salzburg, Marianne Ewaldt asked me if the labyrinth was included in the flower of life. She gave me a small anniversary publication for the 80th birthday of Dr. Siegfried Hermerding, which was titled “The Flower of Life and the Universe”. It contained countless symbols and prototypes, but not a labyrinth.

Ariadne's Thread in the Flower of Life

Ariadne’s Thread in the Flower of Life

This is the picture to which I drew Ariadne’s thread for the three-circuit labyrinth on 25 June 2012 in Salzburg.

What is it about the flower of life? A sober and rational answer comes from Wikipedia :

An overlapping circles grid is a geometric pattern of repeating, overlapping circles of equal radii in two-dimensional space. Commonly, designs are based on circles centered on triangles (with the simple, two circle form named vesica piscis) or on the square lattice pattern of points.

Patterns of seven overlapping circles appear in historical artefacts from the 7th century BC onwards; they become a frequently used ornament in the Roman Empire period, and survive into medieval artistic traditions both in Islamic art (girih decorations) and in Gothic art. The name “Flower of Life” is given to the overlapping circles pattern in New Age publications.

Many see much more in the flower of life. They may, but one should not overemphasize. From the labyrinthine point of view, it remains to be noted that it is a grid in which, depending on the size, different labyrinths can be accommodated. They always have a hexagonal shape and a cube-shaped appearance. It’s a style similar to the labyrinths in man-in-the-maze style, as Andreas has explained in several articles.

In the articles mentioned below further drawings and derivations of Andreas and me can be found.

To accommodate a 7-circuit labyrinth in the Flower of Life, you have to extend the grid of full circles, as Andreas has stated. Marianne Ewaldt did that as a ceramic artist and gave me as present such a labyrinth last year.

A Golden Ariadne's Thread in th Flower of Life

A Golden Ariadne’s Thread in th Flower of Life

And here is another drawing of me with all the lines of the labyrinth in a slightly larger grid:

The complete 7-circuit classical labyrinth

The complete 7-circuit classical labyrinth

It can be clearly seen that the outer boundary lines form a hexagon and also depict a cube.

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Further Link

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Dipl. Ing. Norbert L. Brodtmann uses the curvy and tortuous path in the Chartres Labyrinth to demonstrate the possibilities of the robot arm technology he has developed. He transforms the straight lines and radii of the path elements for the way in the Chartres labyrinth in Bezier curves, which he draws in inverse kinematics by a robot.

I was able to provide him with the necessary coordinates for the trajectories from my true-to-scale drawings of the Chartres Labyrinth.

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Further Link

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An interesting labyrinth is reproduced in the book of Kern (fig. 200, p. 119)°. A drawing by Arabian geographer Al Qazvini in his cosmography completed in 1276 is meant to show the ground plan of the residence of the ruler of Byzantium, before the large city of Constantinople was built up.

This non-alternating labyrinth has 10 circuits and a unique course of the pathway. I will show this using the Ariadne’s Thread and the pattern. In my post “From the Ariadne’s Thread to the Pattern – Method 2” (see related posts, below), I have already described how the pattern can be obtained. When deriving the pattern I always start with a labyrinth that rotates clockwise and lies with the entrance from below. The labyrinth by Qazvini rotates in clockwise direction, however it lies with the entrance from above. Therefore I rotate the following images of the labyrinth by a semicircle so that the entrance comes to lie from below. So it is possible to follow the course of the pathway with the Ariadne’s Thread and in parallel see how this is represented in the pattern.

Four steps can be distinguished in the course of the pathway.

Phase 1

The path first leads to the 3rd circuit. The entrance is marked with an arrow pointing inwards. In the pattern, axial sections of the path are represented by vertical, circuits by horizontal lines. The way from the outside in is represented from above to below.

Phase 2

In a second step, the path now winds itself inwards in the shape of a serpentine until it reaches the 10th and innermost circuit. Up to this point the course is alternating.

Phase 3

Next follows the section where the pathway leads from the innermost to the outermost circuit whilst it traverses the axis. In order to derive the pattern, the labyrinth is split along the axis and then uncurled on both sides. As the pathway traverses the axis, the piece of it along the axis has to be split in two halves (see related posts below: “The Pattern in Non-alternating Labyrinths”). This is indicated with the dashed lines. These show one and the same piece of the pathway. In the pattern, as all other axial pieces, this is represented vertically, however with lines showing up on both sides of the rectangular form and a course similarly on both sides from bottom to top.

Phase 4

Finally the pathway continues on the outermost circuit in the same direction it had previously taken on the innermost circuit (anti clockwise), then turns to the second circuit, from where it reaches the center (highlighted with a bullet point).

Related Posts:

°Kern, Hermann. Through the Labyrinth – Designs and Meanings over 5000 Years. Munich: Prestel, 2000.

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In the last post I have introduced the eleven-circuit Cakra Vyuh Labyrinth. Even though the seed pattern has a central cross and also can be easily drawn freehand, it is not a labyrinth in the Classical style. In fig. 1 I show the seed pattern in different variants.

CaVy_SP_var

Figure 1. Variants of the Seed Pattern

Image a shows the original seed pattern, image b the seed pattern in the Classical style, image c in the Concentric style, and image d in the Man-in-the-Maze style.

This figure clearly shows that the original seed pattern deviates from the Classical style. It is true that this seed pattern has a central cross as for instance the Cretan labyrinth also. However in the Cakra Vyuh seed pattern, from this cross further junctions branch off.

This is different in the Classical style. The Classical style consists of verticals, horizontals, ankles and dots. For this, no central cross is required. This page illustrates well, what I mean (left figure of each pair). If a seed pattern includes ankles these lie between the cross arms and do not branch off from them.

The four images in fig. 1 in part look quite different one from each other. So how do I come to the assertion that they are four variants of the same seed pattern? Let us remember that these figures show seed patterns for the walls delimiting the pathway. Now let us inscribe the seed patterns for the Ariadne’s Thread into these figures (fig. 2).

CaVy_SPab

Figure 2. With the Seed Pattern for the Ariadne’s Thread Inscribed

At first glance this looks even more complex. However, if we focus on the red figures, we will soon see what they have in common.

CaVy_SPa

Figure 3. Seed Pattern for the Ariadne’s Thread

The seed pattern represents a section of the entire labyrinth. More exactly, it is the section along the axis of the labyrinth. The turning points of the pathway align to the axis. This can be better seen on the seed pattern for the Ariadne’s Thread compared with the seed pattern for the walls delimiting the pathway.

In all four seed patterns, turns of the pathway with single arcs interchange with turns made-up of two nested arcs. This constitutes the manner and sequence of the turns and is the basic information contained in the seed pattern. In the four seed patterns shown, the alignment of the turns may vary from circular (image a, image d) to longisch, vertical, slim (image b, image c). The shape of the arcs is adapted to the shape of the walls delimiting the pathway. However in all images it is a single turn in alternation with two nested turns.

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