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## The Chartres Labyrinth is self-dual and symmetrical

The Chartres labyrinth has many qualities. For many it is by far the most perfect and beautiful labyrinth.

The special qualities of the Chartres labyrinth are not recognizable at first glance. One must look at it more exactly and try to understand the structure and the principles of its design.

First let us explore the self-duality.

The layout of the Chartres Labyrinth

The circuits in the drawing are numbered from the outside inwards as well as from the inside out (and the same way in the next diagram below).

First we determine the path sequence for the way in, from the outside (0) inwards (12):
(0)-5-6-11-10-9-8-7-8-9-10-11-10-9-8-7-6-5-4-3-2-1-2-3-4-5-4-3-2-1-6-7-(12).

Now we number the circuits from the inside (0) outwardly (12) and then we read the path sequence for the way back:
(0)-5-6-11-10-9-8-7-8-9-10-11-10-9-8-7-6-5-4-3-2-1-2-3-4-5-4-3-2-1-6-7-(12).

We ascertain, they are identical. So the Chartres labyrinth is self-dual, sign of its extraordinary quality.

The rhythm and the pattern of movement of a labyrinth is manifested in the path sequence. In the Chartres labyrinth the path sometimes touches two quadrants, sometimes only one. But never three or even four quadrants. The biggest step width is five (from circuits  0-5, 6-11, 1-6, 7-12). Most often, however, the step width is one. The most typical step sequence in the Chartres labyrinth is for me at the beginning 0-5-6-11 and 1-6-7-12 at the end. One immediately steps inside, reaches quite directly the innermost circuit, then oscillates through the whole labyrinth, and reaches unexpectedly the center from the outermost circuit. This expresses the dramaturgy of this special pattern of movement.

Admittedly, the counting is laborious. But walking the Chartres labyrinth needs no counting. The real experience can also made by walking.

Let us have a look at the rectangle form and give different colors to the circuits. The entrance is at the bottom right and the center is reached on top left. The circuits are numbered in both directions, i.e. from the outside in and from the inside out. The horizontal distances between S, E, N, W, and S in the rectangular form are of no importance, as it shows the structure (Andreas refers to it as the pattern).

The rectangular diagram

Circuit 6 represents the middle in both directions, this is the reflexion axis. The green and the blue fields are alike. Rotation and shifting shows that they are self-covering. The yellow fields are the connecting elements. They run step-shaped in serpentines.

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### 5 Responses

1. […] The Chartres Labyrinth is self-dual and symmetrical […]

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2. […] 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 […]

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3. Dear Sam,
thank you once more for your contribution.
It is very interesting to see how you dipped into the labyrinth, especially in the 3D dimension. There is a lot of stuff you shared in your comment. It will take time to study and follow that.
If you would like to do, I would invite you to write (as a guest author) some posts on this blog for other labyrinth enthusiasts.
Kind regards,
Erwin

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• on January 5, 2014 at 9:49 pm | Reply Samuel Verbiese

Grateful thanks for this kind suggestion, dear Erwin, I’d love to, but for the time being I’m really behind on lots of deadlines, and in need to study myself all the interesting material you provided with Andreas: material that fits right in the middle of my own wandering and certainly will expand it !
I would appreciate it if you people could ever find some time to read the stuff, see along which roads I started to imagine a ‘credible, logical’ path -yet not necessarily the real hidden one (!)- that brought the early spiral to Chartres and beyond, and, please, especially share your impressions, remarks and recommendations on this humble yet exciting search. I find indeed few people interested as much as you are in the geometrical developments, so constructive discussions would already be a nice start !
Tx and kind regaeds,
Sam

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4. on January 5, 2014 at 5:51 pm | Reply Samuel Verbiese

Dear Erwin and Andreas,

This is interesting, and yes, it haunts my thinking for ten years, first on my own: after discovering Chartres (thanks to Charles Fontaine) that looked beautifully symmetrical, but wasn’t and needed a more simple modelization, I entered it ‘as an engineer’, and after discovering there was only one line straight from the outside to the center, on the ‘wall’, I cut the ‘disc’ just there, and unfolded it in a rectangle then compressed it into a square to discover a ‘pilgrim step’, ‘à la Echternach pilgrims’. I only later found out when searching the web that much was already described before ‘here and there’, albeit in other terms.
This duality indeed proceeds from the meander.

Please see (and please comment !) my progression through my papers at the Bridges conferences now available on-line, starting with the one of Donostia 2007 (after my first poster at Isama-Bridges Granada 2003): http://archive.bridgesmathart.org/2007/bridges2007-405.pdf,
http://archive.bridgesmathart.org/2009/bridges2009-321.pdf, http://archive.bridgesmathart.org/2011/bridges2011-531.pdf,
http://archive.bridgesmathart.org/2012/bridges2012-533.pdf, also the published participations to the Bridges Art-Math Exhibits.

They describe the successive ‘definitions’ of what I call the miniChartres (circularized 7-circuit CCC Classical/Cnossos/Cretan labyrinth with the Chartres ‘opposite returns’ perhaps suggested to the Middle Ages scholar monks, from the ancient Roman mosaic labyrinths featuring that ‘central cross’ that could handsomely replace the lost excentered ‘cross’ of the non-circularized seed of the CCC), and the 3-circuit µChartres (where the quarter-circles of the seed were discarded, and where the cross, in fact a 4-arms star, here must be replaced by a 3-arms star, due to the sparcity of information).
The Chartres ‘doubling’ of the 4 original dots of the CCC seed was also a breathtaking finding by the monks, as this was the way to render the Chartres infinitely extendable, the first step being materialized in the Saffron Walden labyrinth in the UK, with three multiple ‘rings of circuits’ instead of the Chartres two.

No doubt all your nice posts I must study will further feed this shared interst in the geometry of labyrinths stemming from CCC, to Chartres to beyond…
Tx and kind regards,
Sam

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