In the preceding parts the meander row was used or different types were combined. Now an other kind of the combination should be expressed.
In a meander the first line (called “0” in the sequence) is the surroundings of the labyrinth, the place where the way starts. The last line is already the center, where the way ends. In a meander row the first line and the last line of an element are “overlaid”. This line forms a circuit more when a labyrinth is generated from it. However, one can leave out this line and add directly the next element, even mirrored or turned around.
I already used such a meander in my first post about the construction of a labyrinth from a meander without overlooking, however, the whole connections.
To read up in the post from January 6, 2012: How to Turn a Meander into a Labyrinth.
Here once again the first transformation:
I take the meander type 4 and add a rotated meander of the same type without “interlink”.
I get a 6 circuit labyrinth with 4 turning points and the path sequence 0-3-2-1-6-5-4-7.
A 6 circuit Knidos labyrinth
This is a 6 circuit classical labyrinth with a bigger middle. One could call it also Jericho labyrinth, because these have only 6 circuits and consequently 7 walls.
This alignment have been found up to now in no historical labyrinth. How could one name it correctly? The statement about the path sequence only is not enough.
Furthermore I have discovered that it is possible to change the direction of a circuit and to cross the axis while developing a labyrinth directly from the path sequence. This leads to different labyrinth forms with the same path sequence. (Andreas Frei calls it different patterns).
For the above mentioned path sequence there is still an other possibility to construct a labyrinth. It looks thus:
A 6 circuit Knidos labyrinth with “crossed axis”
Besides, the main axis is “crossed” when turning from the first to the sixth circuit. I practically circle around the center and shift the following changes of the course to the other side.
Then, however, the meander from the previous example is not appropriate any more. (Andreas Frei has generously drawn my attention to this fact).
The appropriate meander as a picture of the angular thread of Ariadne arises only afterwards and could look like on top.
The labyrinth is another type than the previous one in spite of the same path sequence.
This alignment is known in historical labyrinths.
In the catalogue of Andreas Frei this type is called “St. Gallen“.
Now I combine the meander type 6 and type 4 in this way.
I will get a 8 circuit labyrinth with 4 turning points and the path sequence 0-5-2-3-4-1-8-7-6-9.
A 8 circuit Knidos labyrinth
To my knowledge this alignment was not used in historical labyrinths, and up to now no labyrinth was built with it. So we have a new type.
As before there is an other variation possible, however, we leave it out.
I take once again meander type 4 and join three of them without “interlink”.
I get a 9 circuit labyrinth with 6 turning points and the path sequence 0-3-2-1-6-5-4-9-8-7-10.
A 9 circuit Knidos labyrinth
To my knowledge this alignment was not used in historical labyrinths, and up to now no labyrinth was built with it. So we have a new type.
As one sees, (almost) no limits are set to the imagination and still many combinations are conceivable.
Now it is a matter rather of finding out or realize the nicest or “walking-friendliest” of all these new types.
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Erwin
Interesting approach to draw the Ariadne’s Thread in the rectangular form for labyrinths with the way crossing the axis (e.g. St.Gallen).
You add one transformation in the rectangular form (RF). The RF is the result of a transformation of the (circular) baisc form. In this transformation, the path segment that traverses the axis is split and comes to lie on both outer sides of the RF. I draw this path segment with two dashed lines in the RR. Thus the RF is made up of two figures that belong together. They have to be thought as connected by the dashed lines. In your RF you shifted those two separate figures against each other until the lines representing the path segment that crosses the axis completely overlap. By this, you unify the separated path segment. However this causes an other separation as some of the circuits are now aligned below and others above the line that represents the traversing pathway.
There are two more differences. I draw the RF in vertical, you draw it in horizontal orientation. Also I do not draw the levels 0 (surround) nor the center of the labyrinth as these are no circuits.
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Thank you, Andreas
for commenting the post.
I know that our rectangular forms are different. I wanted to show above all Ariadne’s Thread as a uninterrupted line.
And I draw it in horizontal orientation and add 0 and the number of the center to make more clear the relationship between labyrinth and meander.
In any way sometimes it is hard to understand the labyrinth displayed in other forms.
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I’ve noticed most of your labyrinths dive into a number (3, 5 or 7) and then work their way back before diving again. I tried to figure out a pattern that would go to a deeper circuit first. I came up with a 3-4-5-2-1-6-11-10-7-8-9-12.
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Yes, Josh, you are right. It is possible to make a labyrinth with the path sequence you have found. As it follows the rules to change between odd and even numbers and to begin with an odd number. You have composed your 11 circuit labyrinth from two 5 circuit labyrinths with the path sequence 3-4-5-2-1-6 for the first and 5-4-1-2-3-6 for the second. Thank you.
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Thank you for these online lessons. I’d never thought of labyrinths as an act of composition. I think I found one to my liking at 3-4-7-8-1-2-5-6-9. You draw it from the same grid as the classic labyrinth, but with an extra long vertical axis up the middle separated by a vertical path. Even though that makes a long lane up the middle, it has some symmetries that play off it well, and it wanders in and out nicely. Still haven’t quite wrapped my head around Ariadne’s Thread and axis crossing. Naja, immerhin.
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Thank you, Josh
for your new found alignment for a labyrinth.
This shows that there still is more to discover on the labyrinthine path.
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