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Posts Tagged ‘7 circuit labyrinth’

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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Beside the oldest known labyrinth with 7 circuits (called the classical one) there are even other variations. Tony Phillips as a mathematician dealed with the question and found 42 different possibilities. Till present 41 of it have not yet appeared as a historical labyrinth.

Andreas Frei has still presented in an article (see below) six of the very interesting examples.

I would like to introduce here 8 labyrinths from the 42 possible variations, according to other criteria. Including the classical one and one still presented by Andreas Frei (Fig. 3), but 6 other, up to now unknown examples.

As is well known (at least now) one enters a labyrinth only on an odd circuit, that is lane 1, 3, 5 or 7. The examples with entrance on the 1st or 7th lane are not so interesting, hence, I have dropped them. Under the aspects of movement and design I like best the access on the 3rd or 5th lane. In the classical labyrinth one begins with circuit 3.

One is immediately inside the labyrinth, is quickly nearby the center, and changes direction in a pendular movement. Quite as Hermann Kern quoted it in his form principles for a labyrinth under >principle detour<.

Since thousands of years there is only one type for a 7 circuit labyrinth known and used until today. This classical labyrinth as a geometric figure has surely been developed from a seed pattern. Maybe one or another new type will appear under the labyrinths of our time? There is still development potential.

The distinction of a type happens through the path sequence. It describes best  the rhythm of the movement.
In the drawings the walls (in black) and the paths (in white) are  equally wide. The middle amounts to the four-fold path’s width. The vertical alignment adjusts to the center axis.
The rectangular diagram is the picture of the path (Ariadne’s thread, here in black) in linear shape and shows the internal structure of the labyrinth. You may read it from the left tot the right.

0-3-2-1-4-7-6-5-8

0-3-2-1-4-7-6-5-8

0-3-2-1-4-7-6-5-8

0-3-2-1-4-7-6-5-8

The “original” classical labyrinth has four turning points and the lines are connected with two consecutive meanders. It can be drawn from the basic pattern or developed from a meander. It is the “mother” of all labyrinths. It is also self-dual, proving thus its high quality.
0-3-4-7-6-5-2-1-8

0-3-4-7-6-5-2-1-8

0-3-4-7-6-5-2-1-8

0-3-4-7-6-5-2-1-8

The further labyrinths have partially another number of turning points and the lines are connected in different ways.
0-3-4-5-6-7-2-1-8

0-3-4-5-6-7-2-1-8

0-3-4-5-6-7-2-1-8

0-3-4-5-6-7-2-1-8

0-3-6-5-4-7-2-1-8

0-3-6-5-4-7-2-1-8

0-3-6-5-4-7-2-1-8

0-3-6-5-4-7-2-1-8

0-5-4-3-6-7-2-1-8

0-5-4-3-6-7-2-1-8

0-5-4-3-6-7-2-1-8

0-5-4-3-6-7-2-1-8

0-5-6-7-2-3-4-1-8

0-5-6-7-2-3-4-1-8

0-5-6-7-2-3-4-1-8

0-5-6-7-2-3-4-1-8

0-5-6-7-4-3-2-1-8

0-5-6-7-4-3-2-1-8

0-5-6-7-4-3-2-1-8

0-5-6-7-4-3-2-1-8

0-5-6-7-4-1-2-3-8

0-5-6-7-4-1-2-3-8

0-5-6-7-4-1-2-3-8

0-5-6-7-4-1-2-3-8

The last drawing in my list is the only further self-dual one. It also belongs to the group of  the six very interesting labyrinths in the article of Andreas Frei.
It is very dynamic and the steps have a bigger spread than in the well-known classical labyrinth. The step sequence, the shift from one circuit to another, is as follows 5f(orwards)-1f-1f-3b(ackwards)-3b-1f-1f-5f. You may read this from the path sequence 0-5-6-7-4-1-2-3-8.
In the well-known classical labyrinth with the path sequence 0-3-2-1-4-7-6-5-8 the step sequence is 3f-1b-1b-3f-3f-1b-1b-3f.
One can experience the rhythm and the “feeling” of a labyrinth by walking it.

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This beautiful labyrinth was a great surprise at Christmas 2007. It belongs to a crib, which was a gift of Mario. He invented the shape all alone.

Heart Labyrinth

Heart Labyrinth

It is a classical labyrinth with 7 circuits and the 4 turning points. They are not arranged in a square, but shifted totally. Also the center is not in the center, but in the left part.
It would be a good exercise to follow the way through the labyrinth with your eyes or with your mouse. And feel what this is doing inside yourself.
Who would like to make a walkable labyrinth out of it?

Crib 2007

Crib 2007

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