The seed pattern to draw Ariadne’s thread, discovered by Gundula Thormaehlen-Friedman, invites to play with it. To try simply to draw more or less curves, to fix the middle somewhere else and so on. And then to look whether a “right” labyrinth is made or not. The matter with the “right” labyrinth is not so easy at all. No dead ends may occur, this is clear. The way should change the direction, he should approach to the middle. He may also lead away in between, at last, however, the middle must be attained.
And thus I have simply tried what happens if I shift the goal one “unity” to the right. I will show the result here and I allow myself to call it snail shell labyrinth. Since the alignment and the form makes me think of a snail shell.
I immediately choose the square form, so that I can draw it geometrically correct. “Z” is not the upper end of the bigger arc as it is in the classical seven-circuit labyrinth, but the end of the small arc, it moves slightly to the right. Then I number consecutively to the right and to the left downwards from 7 to 1. At the end a curve end is left, this is “A”, the beginning of Ariadne’s thread.
First I extend the right square side and the left square side downwards, and the upper one to the right and to the left. By drawing the joining arcs I consider the different centres M1 – M4 in the lower part and “Z” in the upper part. In the end I connect all same-named arc ends by drawing arcs around “Z”. At last I draw a vertical line down from “A”.
All curve ends of the same name are connected strictly and outside around the middle “Z”. This is so to speek the formula.
The circuits are numbered from the outside inwards in ascending order. The sequence of the pathways is the following: 1 – 2 – 5 – 4 – 3 – 6 – 7 – Z. First one walks around completely, then inwards with a jump from the 2nd to the 5th ring, then again outwards to the 3rd ring, and then only forwards to the centre. This is quite an other rhythm as in the classical labyrinth.
The labyrinth reminds me of a snail shell because the entrance lies on the side and far from the centre, and one walks sometimes in the same direction, at the end even spiral-shaped. But it is a “real” labyrinth because all criteria are applicable to it.
Indeed, I have not yet seen such a labyrinth. Who starts and builds one?
Here is the design drawing for a snail shell labyrinth with a dimension between axes (path width) of 1 m.
It is scaleable and can be adapted to other widths. Simply multiply all measurements by the corresponding factor. 1 m width x factor 0.6 results in 0.6 m width; the radii, lengths, and all measurements in the drawing are to be multiplied by 0.6 and will show the new radii, lengths and all other measurements.
Please go to the previous (older) posts on this blog
…and Happy Newyear, despite puzzling times…
Very interesting and clever nice, Dear Erwin !