A Robot Draws Ariadne’s Thread in the Labyrinth of Chartres

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 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

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 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 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 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 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

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)

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

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

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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