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## Posts Tagged ‘Chartres labyrinth’

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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## How to make a Classical (Minoan) Labyrinth from a Medieval Labyrinth, Part 3

Quite simply: By leaving out the barriers in the minor axes. I have already tried this with the Chartres labyrinth some years ago. And in the last both posts on this subject with the types Auxerre and Reims. You can read about that in the related posts below.

Today I repeat this for the Chartres labyrinth. Here the original in essential form, in a concentric style.

The Chartres labyrinth

The original with all lines and the path in the labyrinth, Ariadne’s thread. The lunations and the six petals in the middle belong to the style Chartres and are left out here.

Now without the barriers in the minor axes.

The Chartres labyrinth without the barriers

All circuits can be included in the labyrinth originating now, differently from the types Auxerre and Reims. The path sequence is: 5-4-3-2-1-6-11-10-9-8-7-12. We have eight turning points with stacked circuits. It is self-dual. That means that the way out has the same rhythm as the way in.

But this 11 circuit labyrinth is quite different from the more known 11 circuit labyrinth, that can be generated from the enlarged seed  pattern.
Since this looks thus:

The 11 circuit labyrinth made from the seed pattern

The path sequence here is: 5-2-3-4-1-6-11-8-9-10-7-12. We have got four turning points with embedded circuits. It is developed from quite another construction principle than the Chartres labyrinth. However, it is self-dual.

Now we turn to the complementary labyrinth.

The complementary labyrinth is generated by mirroring the original. Then thus it looks:

The complementary Chartres labyrinth

The entry into the labyrinth happens on the 7th circuit, the center is reached from the 5th circuit. The barriers are differently arranged in the right and left axes, the upper ones remain. It is self-dual.

Without the barriers it looks thus:

The complementary Chartres labyrinth without the barriers

The transformation again works, as it does for the original. The path sequence is: 7-8-9-10-11-6-1-2-3-4-5-12. Also this labyrinth is self-dual.

We confront it with the complementary labyrinth, generated from the seed pattern.

The complementary 11 circuit labyrinth made from the seed pattern

The path sequence on this is: 7-10-9-8-11-6-1-4-3-2-5-12.
Contrarily to the original this type did not show up historically.

So we have created two completely new 11 circuit labyrinths from the Chartres labyrinth, which look different than the 11 circuit labyrinths that can be developed from the seed pattern.

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## How to make two Chartres Labyrinths from one Chartres Labyrinth

The Chartres labyrinth occurs in many variations. Here I speak of the 11 circuit Chartres labyrinth as a type. Some elements of the original labyrinth in the Cathedral at Chartres, such as the six petals in the middle and the lunations  around the outermost perimeter, belong to the style Chartres.

For me the type Chartres exists above all in the layout of the paths.  One goes in quickly (on the 5th circuit) and one quickly approaches the middle (6th and 11th circuit). Then follows the wandering through all quadrants. The access of the centre happens from completely outside (1st circuit) quickly about the 6th and 7th circuit into the centre.

Theoretically there are lot of possibilities to build similar types to the Chartres labyrinth. They can be found worldwide. However, the original Chartres labyrinth owns many special qualities which make it an extraordinary example among the Medieval labyrinths. Among others, it is self-dual and symmetrical.

Layout of the 11 circuit Chartres labyrinth

Hence, the original can be divided in labyrinthine mathematics (11:2=5) in two equal labyrinths. I cut it into two parts, by omitting the 6th circuit. Thereby I get two new, yet identical 5 circuit labyrinths in a Chartres-like layout: I quickly reach the middle and finally enter the centre directly from the outermost circuit. The way in between shows the labyrinthine pendular movement, that Hermann Kern describes as characteristic for a labyrinth.

Layout of the 5 circuit Chartres labyrinth (Demi-Chartres)

How should we now name this type of labyrinth? To me the name 5 circuit Chartres labyrinth seems properly to differentiate it from other 5 circuit Medieval labyrinths with another layout for the paths.
I would like to call it Demi-Chartres.

Just now you may see a nice example for the practical realisation in Vienna on the Schwarzenbergplatz in the temporary plant labyrinth to the European Year of Cultural Heritage 2018:

The temporary plant labyrinth on the Schwarzenbergplatz at Vienna © Lisa Rastl

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## A Modern Walk-Through Labyrinth

The Babylonian visceral labyrinths have found entrance in the modern medicine. In quite an unusual way. A labyrinth-like chip serves for the diagnosis of cancer cells in the blood. The labyrinthine arrangement of the fluid channels shows up to be an effective tool to isolate circulating cancer cells in the blood. That means that the curvature and the tortuous route in the labyrinth is especially useful.

Labyrinth-Chip, Photo courtesy of the University of Michigan, © Joseph XU, Michigan Engineering Communications & Marketing

What kind of labyrinth is this now?
At first sight it reminds of a medieval labyrinth, as it is the famous Chartres labyrinth. It has ten circuits in three sectors, in one these are eight. They will not be traversed one after the other, but reciprocally. And then it has two accesses: An entrance and an exit. It is a walk-through  labyrinth as we know that of the Babylonian labyrinths. Hence, we have an own, new type. And we see the pathway in the labyrinth, Ariadne’s thread. This reminds us of the Greek myth of the Minotaur, which is to be combated like cancer here.
If the Babylonian visceral labyrinths served for the divination, here the labyrinth serves the medicine.
This reminds me of “Ancient Myths & Modern Uses“, the book about labyrinths of Sig Lonegren.

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## The Latvian Pavement Labyrinth Type Chartres at Valguma Pasaule

During the labyrinth congress in Latvia I could also experience a pavement labyrinth type Chartres besides the classical labyrinth and the Baltic wheel. Vita and Viesturs put it on in 2010 beyond the property on a meadow at the edge of the forest. The photo of a similar labyrinth in the gardens of the world in Berlin Marzahn was obviously taken as model for this labyrinth. They probably did not have an exact plan. Thus I have taken some measurements and developed this drawing:

The layout

The paths and the limitation lines are each 40 cm wide. The paths are formed by 6 rows of bright granite stones, the limitation lines by 7 rows of dark stones. The middle has a diameter of 1.80 m, built of 8 rows of bright stones and the center piece measures 80 cm in diameter. The center piece is formed by one single plate of reddish granite with a width of 80 cm and has a slightly convex shape.

The paths and lines are framed by 7 rows of dark stones in a width of about 77 cm. The paved surface has therefore a diameter of 21 m. A 2.50-m-wide way from grit joins this, surrounded by bigger fieldstones.
The path length from the outside up to the central midpoint amounts to a total of 371 m.

The labyrinth ist to be recognized on Google Earth. The geographic coordinates are N 56° 58′ 55″, E 23° 18′ 9″.

Aerial view

Here are some photographic impressions:

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## What’s the Use of the Pattern?

Many of those who are involved with labyrinths use the rectangular form, e.g. Jo Edkins, Niels Mejlhede Jensen, some authors in Caerdroia and many others. Erwin and myself have used it in many posts on this blog. Not all use the same rectangular form and not all use it the same way. However they all intend to achieve a better understanding of the labyrinth. In the following I show some examples with the rectangular form of the Chartres labyrinth.

Figure 1

Thorn Steafel (fig. 1) uses the rectangular form for the walls obtained with method 1 in order to compare the patterns of the Chartres and the Bayeux labyrinths (Steafel T. Reappraising the Bayeux Labyrinth. Caerdroia 2014; 43: 40-45).

Figure 2

Jo Edkins shows on his website the rectangular form  for the Ariadne’s Thread using method 1 and analyzes the course of the pathway (fig. 2).

Figure 3

The same rectangular form (for the Ariadne’s Thread, applying method 1) is used by Erwin in this post (fig. 3). He analyzes the course of the pathway and the duality. This latter can be seen in the different numberings of the circuits on the left and right outer sides. In all three rectangular forms obtained with method 1, the entrance is at bottom right and the center on top left.

Figure 4

Since it can be read from top left to bottom right, I always use the rectangular form for the Ariadne’s Thread obtained with method 2 (fig. 4). This is the form I refer to as the pattern.

Figure 5

Actually, Niels Mejlhede Jensen uses also the rectangular form for the Ariadne’s Thread obtained with method 2 (fig. 5). However, he starts from a labyrinth the main axis of which is oriented to the right. Therefore, his version of the rectangular form stands on one of the outer sides, the arms are represented in horizontal, the circuits in vertical order. The rectangular form or pattern shows the essential of a labyrinth without confusions that may be caused by circular or polygonal layouts, varying lengths of circuits, decorative artwork etc. This is useful for

• the analysis of the course of the pathway. This may serve for further purposes such as
• comparing labyrinths in order to identify communities or differences between labyrinths
• presenting the inner structure and particularities of specific labyrinths
• the research of relationships between different labyrinths
• the demonstration of an important general property of labyrinths: the duality

The pattern provides an unambigous criterion for grouping similar and distinguishing between different labyrinths.

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## The Chartres Labyrinth: The Long and Winding Way to the Middle

Recently you could read something about the long and winding path in a classical labyrinth.
Today we want to look more exactly at the path in the Chartres labyrinth. This is quite an other type of labyrinth. It has more circuits than the Cretan labyrinth, eleven instead of seven.
We orientate by the original, that is since about 800 years on the floor inside the cathedral of Chartres. The ways are much smaller than they should be for a “open land labyrinth”.
It depends not only on the type labyrinth, how long the ways are, but also from the constructive form. So: How wide the ways are, how wide the boundary lines are in between, how big the middle is etc.
In the Chartres labyrinth we have a distance of 42.6 cm from axis to axis.

From A to Z: The long and the short path

The direct way from “A” to “Z” straight across all boundary lines to the center of the Chartres labyrinth amounts to 6.45 m. This corresponds to half a diameter of 12.90 m.
The whole, long way from the entrance into the center amounts to 263.05 m by following all the turns. This proves a relation between the long and the short distance of 263.05: 6.45 = 40.78. So a much higher “detour factor” than in the Cretan labyrinth.

If I handle the thread at the beginning and at the end and stretch it apart, I will get a straight line which reaches from “A” to “Z” and which corresponds to the way into the middle, that is 263.05 m.
If I join together the beginning and the end, I will get a circle. The circumference corresponds to the straight line of 263.05 m. The diameter would be 83.73 m.
I can also make a square with the same size from it. Then this would have four side lengths of 65.76 m.

The following drawing, yet not true to scale, illustrates the different figures and the true ratio among each other: