What is Special about the Nîmes Labyrinth

In my last post I have pointed to the special layout of this roman mosaic labyrinth (see related posts below).

Figure 1. Mosaic labyrinth of Nîmes

Figure 1. Mosaic labyrinth of Nîmes

In the meantime I had a closer look at it and found six peculiarities.

Figure 2. The Peculiarities

Figure 2. The Peculiarities

  1. Here, there is no diagonal (as opposed to the 3 fine dashed lines from the middle to the other three corners). Along each of these diagonals, the pathway is bent by 90° degrees. Therefore, all circuits only make three bends of 1/4 of a circle.
  2. Accordingly, the turns of the pathway that normally lie beyond the axis (on the side opposite to the entrance) are oriented horizontally, not vertically.
  3. Moreover, they are not arranged in one line as normally, and as are the turns of the pathway on this side of the axis too.
  4. The three inner circuits (circuits 5 – 7) lie entirely on this side of the axis and thus cover only quadrants 1 and 2.
  5. Correspondingly, quadrants 3 and 4 are only covered by the four outer circuits (circuits 1 – 4).
  6. And, as if this were not enough, the center makes one exception. Instead of entering the center axially, the pathway makes one additional turn of 1/4 of a circle before it reaches the center. Therefore it enters the center in parallel with the way into the labyrinth. First I thought, the designer might have wanted to mislead the observer about the true 3/4 – nature of this labyrinth. A closer look at it, however, reveals, that this last turn of the pathway is an inevitable result of the chosen layout for the course of the pathway.

It surprises me again and again how interesting some of the historical labyrinths are.

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Variants of the Cretan Labyrinth

How to Draw Variations on the Snail Shell Labyrinth, Part 2

Today we will see the Snail Shell labyrinth in square form.
We build the labyrinth by strictly using the given path sequence, but we don’t cross the central axis. Thus the path several times changes the direction. This again produces the pendular movement how it is demanded for a “right” labyrinth. There arise four turning points.
A more exact view also shows the hidden type Knossos inside, and that only at the beginning and at the end two circuits with change of course were added. Andreas has already pointed to that.
The following drawing shows the walls in black, the seed pattern is highlighted in colour.

The Snail Shell Labyrinth with 4 turning points

The Snail Shell Labyrinth with 4 turning points

Nevertheless, another new type of labyrinth turned up indirectly via the derivation of the Snail Shell labyrinth from the seed pattern by the construction after the path sequence. Though with the creative defects of the beginning on the first circuit and the entry into the middle from the last circuit. However, at least, it is self-dual.
The seed pattern for this type I developed belatedly. It looks quite different as the meanwhile well-known pattern for the Classical 7 Circuit Labyrinth.


Much different looks the labyrinth if one uses all the four crossings of the axis which are possible, even though keeping up the path sequence.

The Snail Shell Labyrinth with 2 turning points

The Snail Shell Labyrinth with 2 turning points

There remains only two turning points with changes of direction: When changing from the 5th to the 4th circuit, and when changing from the 4th to the 3rd. For the rest one advances forwards in a spiral-shaped movement, just as in a snail shell.
If one arranges the entrance edgeways, one can fill up the whole square. One could still procreate other shapes by twisting and mirroring the figure.

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How to Draw Variations on the Snail Shell Labyrinth, Part 1

The “original” Snail Shell labyrinth was created from the seed pattern for Ariadne’s thread. To do that only the first curve to be drawn had to be shifted one “unity” to the right. Then all points were connected with each other. Thus a new type for a 7 circuit labyrinth appeared.

However, this type can also be derived from the well-known seed pattern for the walls. The construction goes as usual, only that everything is shifted to the right.
The following drawing shows the walls in black, the seed pattern is highlighted in color.

The Snail Shell Labyrinth made from the seed pattern

The Snail Shell Labyrinth made from the seed pattern

In the meantime, Andreas has also posted something to this labyrinth. He has explained the pattern in the labyrinth, and has pointed to the fact that the path crosses twice the axis. Thus, in the terminology of Tony Phillips it is a non-alternating uninteresting Labyrinth.

The “pattern” is for Andreas not the seed pattern, but the structure of the labyrinth, as best to be seen in the rectangular form.  Hence, “uninteresting” in the terminology of Tony Phillips means that inside this labyrinth the type Knossos is hidden to which only some circuits are added. And the fact that one enters the labyrinth on the first circuit and reaches the middle from the last one.

For me it is interesting that developing the Snail Shell labyrinth from the seed pattern produces the cruising axes. This is ordinarily not the case when using this method. Nevertheless, a new type of labyrinth appears.


If one constructs a labyrinth by only using the path sequence, and without cruising the axes, one will get another labyrinth again. Thus it looks:

The Snail Shell Labyrinth made from the path sequence

The Snail Shell Labyrinth made from the path sequence

This is quite an other type of labyrinth, although it has the same path sequence. Moreover, it is self-dual, because you may count the circuits from inside outwards and you will get the same path sequence.
This shows once more that only the path sequence is not sufficient to classify the type. Unfortunately, I must say, because this makes the categorization even more difficult and more complicated.

One receives even more variations if one includes the crossing of axes or chooses other forms (circle, square). Of which more later.

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How to Make Seven New (up to now unknown) 7 Circuit Labyrinths on Snow

A way is made by walking it. This is applicable all the more for the labyrinth. And on snow this is especially nice – and simply possible. Thus I tried to put into practise the theoretical / mathematical considerations of the last blog entries.

For that to happen, I memorized the path sequence of the respective thread of Ariadne, and repeated it over and over again like a mantra while trampling the path into the  snow. And I counted in which circuit I just was and which was the next to come. For one have to pay attention where and what circuits will be made later,  and leave enough place for them. Having a look at the providently printed drawing of the prototype before tracking the path will help.
After arriving the center I traced back one more time the whole long way to the beginning what was sometimes quite strenuous. One should not change the lane, this is a point of honor. And if one makes the distances between the single circuits greater than a hop, this is likewise not possible.

I have tried to implement all 7 new types. I have made some more often. My “favorite type” is at present 5674 1238. The path sequence as an eight digits figure can be noticed quite well in two groups of four. Then the well-known classical labyrinth would be e.g. the type 3214 7658.

Who wants, can investigate more exactly the different types in the below quoted post. And if someone liked to experience the path on one’s own, he may copy and print the drawings.

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