In the meantime, I have developed for myself a method to construct a labyrinth by only using the path sequence. I do not apply the seed pattern to do that.
I would like to show this here for a 7 circuit classical labyrinth with the path sequence 0-3-2-1-4-7-6-5-8. It is from an other shape as the usual classical labyrinth and was to be seen in a previous post.
First I draw freehand the path of the labyrinth (Ariadne’s thread) according to the path sequence. To get an other shape, I cross the main axis with the 4th and the 7th circuit. From the sketch I derive the number of the turning points and the construction lines. Then I count the number of the ways between the central point and the turning points which are also centers in the further construction.
The broad for the paths and the walls is the same with 1 m, this makes a dimension between axes of 2 m. The diameter of the middle is the fourfold dimension between axes. The lengths of the different construction lines are calculated from this details.
I begin with a horizontal line (M2 – M3) and I fix the central point M1 by applying the two distances from M2 and M3. In the same way the other points are defined. (Fig. 1)
Starting from the center M1 I draw auxiliary circles in an interval of 1 m from the inner to the external diameter. (Fig. 2)
The lines M1 – M2 and M1 – M3 are extended up to the external diameter, also the lines M2 – M4 and M3 – M5. (Fig. 3) They are limiting the circular arcs.
Then the different curved sections are drawn with the help of the path sequence in the centers M2 to M5.
In fig. 4 this are the semicircles around the turning points of the ways 5/6 in M2 and the ways 6/7 in M3. The construction is made through connection with the end points of the bigger external arcs.
In fig. 5 the curved sections of the remaining external arcs are formed around the centers M2 and M3.
In fig. 6 follows the connection of the ways 1/2 around M4 and the ways 2/3 around M5.
In fig. 7 the open, innermost pieces of the way are connected by strictly watching the path sequence. These are curved sections which joins each other without sharp bends.
In fig. 8 I turn all curves and lines around the center M1 in such a way that the entry axis for the middle is strictly vertical.
Fig. 9 shows the completed labyrinth. The paths are highlighted in color. The walls have the same broad and are left white. The left blank fontanel is good to recognise. It has another shape as the usual classical labyrinth. It appears when the paths are drawn in constant width.
The drawing is rather a sort of model or template. The labyrinth can still have got different shapes, can be angular or completely round, right- or left-handed. The paths and the walls can be of different widths, also the middle can be bigger or smaller. It is only important to maintain the alignment of the labyrinth.