The St-Omer labyrinth

1  The St-Omer labyrinth.

The black color represents the walls; the path corresponds to the background color. Both are the same width, which may be considered as the building unit.

It may be interesting to note that this labyrinth is built in a square 49 by 49 units, 49 being the square of 7. However, the structure of the design does not seem to reflect these numbers, which tends to suggest that the designers were not interested in exploiting or manifesting them.

2  The Chartres labyrinth in its square version (unknown in the Middle Ages).
The lower center arrangement (closed square, entry centered on the main axis) is from the St-Omer labyrinth which seems to be the only one to have it. It is found in some recent labyrinths (example : Santa Rosa).

Trying to build a square version of the Chartres labyrinth with wall and path the same width, I discovered that it fits in a 49-unit square, as does the St-Omer labyrinth. This is how I came to think of the relationship between those two labyrinths. However, since the medieval labyrinth was first designed to be drawn with compass on parchment manuscripts, in its round version, this mumerical curiosity can in no way be considered to explain its structure nor even the number of its lanes.

3  The parts (of the walls) common to both labyrinths.

4  The elementary modifications.

Each modification can be visualised as a 90° rotation of a wall segment 3-unit long pivoting on its center, in the manner of a double pivoting door. One position corresponds to one of the labyrinths, and conversely.

The hatched texture belongs to the Chartres labyrinth, the dotted texture belongs to the St-Omer labyrinth.

Certain anomalies are visible in the upper center: they result from additional modifications necessary to produce the cross motif.

Other apparent anomalies result from the same "tile" or unit being touched by two adjacent modification cancelling each other. Therefore that tile stays as it was, either wall or path, and does not show a texture.

5  The spatial distribution of the elementary modifications.

This drawing shows the general symmetry of the spatial distribution of the elementary operations producing the transformation. That remarquable symmetry makes it highly improbable that the St-Omer labyrinth could have been developed independently from the Chartres labyrinth. So does also the fact that it is built on a 49 unit square, which also seems to come from the square Chartres labyrinth.