Saturday, July 16, 2011


While trying to develop a cipher based upon the Chartres labyrinth, I struck upon an interesting feature of its layout and construction. While the layout of most labyrinths is well understood and well-documented, the layout of the Chartres labyrinth appears less so. 

For example on this website, which contains impressive work attempting to uncover the secrets of the labyrinth, states that the Chartres labyrinth is 'pseudo-symmetrical'. I believe this statement reveals a profound lack of understanding of the basis of the Chartres labyrinth construction, because, as I shall show you, the labyrinth is perfectly symmetrical under certain transformations.

To prove this all we need to do us to distort the image using its Polar Coordinates, which gives us roughly this image.
 As we can see this schematic is indeed symmetrical via a horizontal axis. This means that it should be possible to completely invert the Chartres labyrinth without distorting any of its pathways or layout. And so it is;
This final test proves that the Chartres labyrinth is indeed perfectly symmetrical. It also shows us that the inside of the labyrinth is the same as the outside. Finally, if we superimpose both the original and inverted labyrinths we get a peculiar floral motif at the centre. Judging by the manner in which the two sections of the labyrinth complement each other in scale, I would say that this correlation was planned. But I don't know what significance, if any, the floral motif has in this instance.
There has been some argument that the Chartres Labyrinth is actually a Solar or Luna-based calendar, and there appears to be some validity to these claims, although just what this means is uncertain. For example, there are 112 lunations around the outer-edge of the labyrinth, which is 28 x 4. This corresponds to a period of 16 weeks or 4 lunar month (of 28 days each). If the Chartres labyrinth is meant to be a calendar, of some kind, it does not serve its function well, as it only contains information for 4 of the 12/13 lunar months.

However, I believe I may have stumbled upon this missing data while trying to devise a method for building a cipher based on the twisting paths of the labyrinth. As you can see the labyrinth is divided into four main sections, which may be used to represent the four seasons of the year. If we count all of the bends in the labyrinth we get 12 (months) and if we include the inside and outside of the labyrinth in our figuring and then count every second circuit in each segment we get a total of 52; the number of weeks in a year.

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