How to Draw a Man-in-the-Maze Labyrinth / 6

Non-alternating Labyrinths

In all previous posts of this series with the exception of the second part (see related posts below) I have shown alternating labyrinths. In alternating labyrinths the pathway does not traverse the axis. However, there exist also labyrinths in which the path traverses the axis (in multiple-arm labyrinths: the main axis). These are termed non-alternating. A beautiful example of such a labyrinth is depicted in a manuscript from the 10./11. century of the Stiftsbibliothek St. Gallen. Erwin has already presented it on this blog, and I have published on it in Caerdroia 38 (2008).

Illustration 1. St. Gallen Labyrinth

Illustration 1. St. Gallen Labyrinth

From part / 2 of this series, we know that in principle also non-alternating labyrinths can be drawn in the MiM-style, as the Snail Shell labyrinth is non-alternating. The pathway of this labyrinth traverses the axis twice. Once when it skips from the first to the second circuit and second when skipping from the second inner to the innermost circuit.

Illustration 2. The Ariadne's Thread

Illustration 2. The Ariadne’s Thread

The pathway of the St.Gallen labyrinth (ill. 2), however, comes in clockwise from the outer circuit, turns to the right and moves axially to the innermost circuit, where it turns to the left and continues without changing direction (clockwise). How does this affect the seed pattern and its variation into the MiM-style of this labyrinth?

Illustration 3. Seed Patterns Compared

Illustration 3. Seed Patterns Compared

Ill. 3 shows the seed pattern of my demonstration labyrinth from part / 5 of this series (figures a and b) and compares it with the seed pattern of the St. Gallen labyrinth (figures c and d). The seed pattern of the demonstration labyrinth has one central vertical line. This represents the central axial wall to which are aligned the turns of the pathway (fig. a). This is the case with all alternating labyrinths. Variation of seed patterns of alternating labyrinths into the MiM-style leaves the central line and the innermost ring untouched (fig. b). The auxiliary figures of alternating labyrinths all have two vertical spokes and an intact innermost ring.

This is different with the labyrinth of St. Gallen. The seed pattern of this labyrinth has two equivalent vertical lines (fig. c). Between these lines the pathway continues along the central axis. If we vary this seed pattern into the MiM-style, we find no central wall and the innermost ring interrupted (fig. d). The auxiliary figure of the St. Gallen labyrinth therefore has no vertical spoke.

Illustration 4. Labyrinth of St. Gallen in the MiM-style

Illustration 4. Labyrinth of St. Gallen in the MiM-style

Non-alternating labyrinths can be drawn in the MiM-style in the same way as alternating labyrinths. The seed pattern of the St. Gallen labyrinth has two elements with single and two elements with two nested turns, and in addition the segment of the path that traverses the axis. In the MiM-auxiliary figure this seed pattern covers two circuits. This corresponds with the elements that are made-up of two nested turns. The pathway segment traversing the axis needs no additional circuit, as for this the innermost ring is interrupted to let the path continue through the middle of the seed pattern.

Illustration 5. My Logo in the MiM-style

Illustration 5. My Logo in the MiM-style

And, finally, here is my logo in the MiM-style (ill. 5).

Related posts:

How to Turn a Meander into a Labyrinth

In one of the preceding articles we identified the meander contained in the classical (Cretan) labyrinth. Now we will go the other way round and turn the meander into a labyrinth. For this purpose, however, we will choose a different form of meander, otherwise it will be too boring.

Meander border

Meander border on a wallpaper at Boies-Lord House (Picture courtesy of © Chuck LaChiusa)

We will draw a scheme of the elements and number the vertical lines from the left to the right. This will be the circuits (the paths). The horizontal lines at the top and on the bottom represent the axis. There are only 6 circuits and not 7 as with the Cretan labyrinth. The path sequence is the following: A-3-2-1-6-5-4-Z. This should be the way leading inside. The way out: Z-4-5-6-1-2-3-A. Totally different from what we are accustomed to.

Scheme drawing meander border

Scheme drawing meander border

On the right element the circuits are numbered from the inside to the outside (of the labyrinth) in the scheme above. The path sequence for the way out is identical with the order for the way in. Besides, the sum of both rows always amounts to 7, which is also the number of the limiting border lines (the walls); see at the bottom right. The labyrinth is self-dual because an identical labyrinth appears when the path sequence is turned around. Moreover, the lower chain of signs is a palindrome because there is always the same chain of signs, whether you read it backwards or forwards.

From the path sequence and the scheme drawing (diagram) I can now deduct the corresponding labyrinth. I choose a round shape and will get  Ariadne’s thread for a 6 circuit labyrinth:

Ariadne's thread (in black) in a 6 circuit labyrinth

Ariadne’s thread (in black) in a 6 circuit labyrinth

I simply established an order of circuits strictly and schematically according to the path sequence. Additionally the centre only disposes of the width of one path. All this does not look very harmonious.

Now I will try to filter the seed pattern out of this labyrinth and to draw a labyrinth on this basis. This time the walls are black. This layout ressembles the look we are used to somewhat more.

The 6 circuit labyrinth with the coloured seed pattern

The 6 circuit labyrinth with the coloured seed pattern

When I look at the seed pattern more closely, I notice that the vertical bar of the cross is split in two by an additional passage, so to speak. The left part of the seed pattern is identical to the well-known seed pattern for the 7 circuit classical labyrinth; the right part is identical to the seed pattern for the 3 circuit classical labyrinth.
So I have put two halves of a seed pattern together and thus creatred a new, different labyrinth.  Or to say it more dashingly: Half a 7 circuit and half a 3 circuit labyrinth result in a 5 circuit one (3.5 + 1.5 = 5). Together with the additional passage this makes a 6 circuit labyrinth.

In order to obtain a more harmonious round labyrinth I will now choose a bigger centre and will not draw the walls in such a pronounced way. This makes the following drawing:

A 6 circuit classical labyrinth

A 6 circuit classical labyrinth

I can state now that the entrance axis and the goal axis lie on one and the same line. As usual I step into the third circuit immediately and then go towards the outside again. But unlike as in the Cretan labyrinth I then go directly from the very outside to the very inside and circle the centre. Then my way leads into the direction of the entrance and from the fourth circuit finally to the centre. The alignment us unusual, but I like it his way. I have never walked such a type of  labyrinth. Does anybody know such a labyrinth? Or who will be the first to build one of this type?

Now there the question arises: Is there such a type of labyrinth known in the history of labyrinths? There is.
So this is not an invention of mine because 1000 years ago someone had already this idea, or at least a similar idea. In Hermann Kerns book we find two examples with this alignment.
According to the suggestions coming from Andreas Frei one would have to call this type >St. Gallen<, because that is the first historical proof.

Type St. Gallen

Type St. Gallen (10th /11th century) Source: Hermann Kern, Labyrinthe, 1982, pict. 209, German edition

In a hand-written parchment from the 10th/11th century kept in the St. Gallen chapter library the round labyrinth can be found as an illustration to a text of  Boethius >Consolation of Philosophy< (around 480 – 524 AC). Obviously the designer wanted to draw a round Cretan 7 circuit labyrinth, made some errors and only drew 6 circuits and erased a lot to obtain a “right” alignment for a labyrinth. (Source: Hermann Kern, Labyrinthe, 1982, p. 176, 177, German edition).

The second labyrinth of this kind appears with the so-called  Jericho Labyrinths where the 6 circuits are to be found with a different alignment altogether.But there is also “our” type as a full-page miniature in a Syrian grammar book belonging to the Bishop Timotheus Isaac, written in 1775, in which the town of Jericho and Joshua are pictured as a labyrinth. (Source: Hermann Kern, Labyrinthe, 1982, p. 197, German edition).

The town of Jericho as a labyrinth

The town of Jericho as a labyrinth (1775) Source: Hermann Kern, Labyrinthe, 1982, pict. 229, German edition

I have turned the drawing so that one can recognize the design more easily. The 7 circuits of the Cretan labyrinth do exist, but the first, outer circuit is not accessible. So there are 6 circuits and an alignment as with the round type of St. Gallen. It is scarcely understandable how the illustrator came up with that layout, but it was certainly not with the method “trial and error”.

Further links

  • There is an article on Wikipedia about the meander, in which are already hints concerning the labyrinth.
    Here the link … >
  • I found the photo with the meander border on the wallpaper on the website of  Chuck LaChiusa. There you can find more photos of other meander types as well as some information related to meander and labyrinth.
    Here the link … >
  • Andreas Frei (Switzerland) is exploring intensively the structure of the labyrinth and has proposed a catalogue with 74 different historical labyrinth types so far. On his website you will find much more information and many basics in order to better understand the different types of labyrinths (in German by now).
    Here the link … >

Note from 01/09/2012:

Andreas Frei told me via e-mail that I am wrong with my opinion to consider my newly developed labyrinth as the type St. Gallen. Because in the St. Gallen labyrinth the path crosses the central axis, what is not the case in my labyrinth. So there are is more than one possibility to build a labyrinth from the same path sequence.