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Archive for the ‘Typology’ Category

This type of labyrinth has already been described and appreciated in detail. Nevertheless, I would like to come back to this today.
I was particularly drawn to the five-pointed star (the pentagram) in the center. This appears in many national flags, so also in the European flag. That is why this type of labyrinth would be well suited for a “European labyrinth”. The Augsburg humanist Sigismund Gossembrot the Elder would also be a good “godfather” for such a labyrinth.

The Gossembrot labyrinth in European colors

The Gossembrot labyrinth in European colors

Here with boundary and path lines of the same width. That would be e.g. well suited as a template for a finger labyrinth:

The Gossembrot fingerlabyrinth in European colors

The Gossembrot fingerlabyrinth in European colors

It would be nice if this type of labyrinth were built as a walkable and public labyrinth.
To make this easier, I present a kind of prototype in the following drawing. The axis dimension is 1 m. This makes it very easy to convert to different sizes. Since the line axes are specified, different line and path widths can be implemented. The diameter of the center is four times the axis dimension, i.e. 4 m.
How this is done with a scaling factor has already been explained in various articles in this blog, most recently in the labyrinth calculator.

The design drawing

The design drawing

Here you can see, print or download the drawing as a PDF file

The rights of use are the same as for the labyrinth calculator.

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The question of a formula or table for calculating the construction elements in the labyrinth has arisen several times. For me, I solved the problem by designing and constructing the various labyrinths using a drawing program (AutoCAD). This creates drawings that contain all elements geometrically and mathematically exactly.
However, I do not print these on a specific scale, but adjust the size of the drawing so that it always fits on a sheet in A4 format.
Only the dimensions are decisive for the implementation of the labyrinth in the location. If possible, I also try not to use “crooked” measurements, but simple units, usually the meter.
The dimensions are therefore suitable to be scaled and so labyrinths can be constructed in different sizes.
The drawings thus represent a kind of prototype. Since the axes of the lines are always given, the widths of the boundary lines and the path can be varied.

The construction elements of the lines in the labyrinth mostly consist of arcs and straight lines. In the program used (AutoCAD), these individual elements can be combined into so-called polylines and their total length is then calculated.

The length specifications for the boundary lines and the path (the Ariadne thread) in the drawing are thus created. The boundary lines consist of 2 straight lines and 22 arcs (24 elements in total). The Ariadne thread consists of 1 straight line and 25 arcs (26 elements in total). The entire labyrinth consists of 50 individual elements.

It would be possible to calculate all of this in a table with the corresponding formulas, but it would be more cumbersome and extensive.

The scaling factor makes it easier to calculate variants in different sizes. The labyrinth calculator is something like a summary and general instructions for use. Here especially for the well-known Classical 7 circuit labyrinth.
However, this method has also been described for other types of labyrinths in this blog.

The Labyrinth Calculator

The Labyrinth Calculator

Here you can view, print or download the drawing as a PDF file

Here are some comments on copyright:
All drawings and photos in this blog are either mine or Andreas Frei, unless otherwise stated, and are subject to license CC BY-NC-SA 4.0
This means: You may use or change the drawings and photos without having to ask us if you name our names as authors, if you do not use the drawings and photos for commercial purposes and if you publish or distribute them under the same license. A link to this blog would be nice and we would be happy, but it is not a requirement.

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We wish all visitors of this blog a Merry Christmas and a Happy New Year!

Christmastree labyrinth

Christmastree labyrinth

The basis for this labyrinth is the labyrinth shown often in this blog, originally rejected by Sigmund Gossembrot on folio 53 v.
Andreas Frei discovered and described the pattern for this new type in his blog posts.
I have taken up this structure and shown it in different ways of representation (= style).
Finally, in this year’s Christmas tree labyrinth in a triangular and centered shape.

One could say in a somewhat sophisticated way: Andreas is the master of the type and I the master of the style.

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I have already seen many pictures of finger labyrinths on the internet. Mostly they are made of wood or ceramics. They show the way in the labyrinth, Ariadne’s thread.
I do not like many of them. Especially the last part of the way, the entrance to the center, is often not so satisfactory. This is not very clear in some finger labyrinths; the path often runs from the side rather than from the bottom and perpendicular to the center.

That’s why I would like to present some own ideas on that.
In the classical 7 circuit labyrinth, the center is usually only as wide as the path itself and therefore less accentuated. That’s why I prefer to choose a slightly larger center, as we have it in the Knidos style. But not four times the axle width, but only the double.

That’s how it looks:

Ariadne's thread in Knidos style

Ariadne’s thread in Knidos style

The turning points are slightly shifted, the center is slightly enlarged. As a result, the last piece of the path runs perpendicular to the center.


In addition, the classical 7 circuit labyrinth can be centered very well. Since the first and the last part of the path are on the 3rd and 5th ambulatory.

That’s how it looks:

Ariadne's thread centered for a finger labyrinth

Ariadne’s thread centered for a finger labyrinth

The four turning points are shifted a bit more.
The empty space in the interior also is a bit more distorted.


Below is a kind of preview drawing for a round labyrinth of 33 cm diameter with all construction elements.

However, the dimensions are very well scalable. That is, for a smaller labyrinth, I use a corresponding scaling factor, which multiplies all measures.

For example, if I want it to be half the size, I multiply all measurements by 0.5.

If I want to reach a certain size, I determine the required scaling factor by dividing this size by 33 cm.

For a desired diameter of 21 cm, e.g. I calculate the scaling factor as follows: 21 cm : 33 cm = 0.636. I then multiply all the measurements with 0.636.

To convert the cm to inches, I divide by 2.54: The diameter becomes 33 : 2.54 = 13 inches.

Note for my inch-using visitors: Simply replace the measure unit “cm” by “inch” in the drawing and then calculate the desired size of your labyrinth as described above.

Design drawing

Design drawing

Here you might see, print or download it as a PDF file

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It seemed obvious to apply the principles for two-parted 5 circuit labyrinths in the previous posts also for 7 circuit labyrinths.

For this purpose, the double barrier is extended to 6 passages, thus creating a triple barrier.

This is what it looks like:

A two-parted 7 circuit concentric labyrinth (entrance 3rd track)

A two-parted 7 circuit concentric labyrinth (entrance 3rd track)

It is noteworthy that both the entry into the labyrinth as well as the entry into the center is possible in and from the same circuit, here from the third circuit.
The path sequence is: 3-6-5-4-7-2-1-2-7-4-5-6-3-8

But it is also possible to design that from the 5th circuit. This creates a new type again.
Here is the example:

A two-parted 7 circuit concentric labyrinth (entrance 5th track)

A two-parted 7 circuit concentric labyrinth (entrance 5th track)

The path sequence is then: 5-4-3-6-7-2-1-2-7-6-3-4-5-8


And here are the two variants in Knidos style:

A two-parted 7 circuit labyrinth in Knidos style (entrance 3rd track)

A two-parted 7 circuit labyrinth in Knidos style (entrance 3rd track)

 

And here from the 5th circuit:

A two-parted 7 circuit labyrinth in Knidos style (entrance 5th track)

A two-parted 7 circuit labyrinth in Knidos style (entrance 5th track)

Now you could move the barrier and its related elements upwards. Then it would not be the first circuit who is completely gone through, but the innermost, the 7th circuit.

So the whole structure (pattern), expressed in the path sequence, would be changed. That would also create a new type of labyrinth again.

Here in a simplified representation:

A two-parted concentric 7 circuit labyrinth (entrance 3rd track)

A two-parted concentric 7 circuit labyrinth (entrance 3rd track)

Here with entrance in the 5th circuit:

A two-parted concentric 7 circuit labyrinth (entrance 5th track)

A two-parted concentric 7 circuit labyrinth (entrance 5th track)

But someone else had this idea. On the Harmony Labyrinths website, Yvonne R. Jacobs has introduced hundreds of new labyrinth designs and copyrighted them.

She calls these types Luna V (Desert Moon Labyrinth) and Luna VI (Summer Moon Labyrinth). On her website you can look at the corresponding drawings and even order finger labyrinths (only in the USA).

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In dealing with the double-barrier technique in recent posts, I found this installation of Mark Wallinger’s Labyrinths on the London Underground:

The labyrinth 233/270 at the station Hyde Park Corner, Photo: credit © Jack Gordon

The labyrinth 233/270 at the station Hyde Park Corner, Photo: credit © Jack Gordon

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

The special feature of this is that two double barriers are located next to each other in the upper part of the central axis. In the routing chosen by him you move at the transition from the 2nd to the 3rd quadrant first away from the center.

I’ve changed that so much that you would “experience” a movement to the center in a walkable labyrinth.

This is what it looks like:

A new labyrinth in concentric style

A new labyrinth in concentric style

I have also moved the side double barriers and this makes the routing in all quadrants also different. So a new type of labyrinth is born.

Here in Knidos style:

A new centered sector labyrinth in Knidos style

A new centered sector labyrinth in Knidos style

Why not as a two-parted labyrinth?

A new two-parted 5 circuit labyrinth

A new two-parted 5 circuit labyrinth

The left part has the path sequence: 3-4-5-2-1 and the right part: 5-4-1-2-3, so there are two 5 circuit labyrinths in it.

And here again in Knidos style:

A new two-parted and centered 5 circuit labyrinth in Knidos style

A new two-parted and centered 5 circuit labyrinth in Knidos style

The remarkable thing about this type is that both the entry into the labyrinth in the 3rd lane takes place, as well as the entry into the center.

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There are eight possibilities for a one arm 5 circuit labyrinth (see Related Posts below).

The structure of the different labyrinths can be expressed through the path sequence. Here is a list:

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

The sector labyrinth presented in my last post (see Related Posts below) has a different path sequence in all 4 quadrants. In other words, there are 4 different labyrinths hidden in it. These were the path sequences in the 1st to the 4th line of the list above.


Today another 5 circuit sector labyrinth modeled with Gossembrot’s double barrier technique:

A new 5 circuit sector labyrinth in concentric style

A new 5 circuit sector labyrinth in concentric style

The path sequence in quadrant I is: 3-4-5-2-1, in quadrant IV: 1-2-5-4-3. These are the aforementioned courses at the 5th and 6th place. The two upper quadrants have: 1-4-3-2-5 and 5-2-3-4-1. These correspond to the upper pathways at the 4th and 3rd places. Not surprising, because the transition in these sector labyrinths takes place either on the 1st or the 5th course.

Here in a representation that we know from the Roman labyrinths:

The new sector labyrinth in square shape

The new sector labyrinth in square shape

Or here in Knidos style:

The new sector labyrinth in Knidos style

The new sector labyrinth in Knidos style

On Wikimedia Commons I found this picture of Mark Wallinger’s unique Labyrinth installation at Northwood Hills station, installed as part of a network-wide art project marking 150 years of the London Underground. It is part of the emboss family (one of the 11 labyrinth design families).

Mark Wallinger Labyrinth 10/270, Photo: credit © Jack Gordon

Mark Wallinger Labyrinth 10/270, Photo: credit © Jack Gordon

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.


Now only two path sequences are missing, then we would have the eight complete.
There is also a new sector labyrinth for this:

Another new sector labyrinth in concentric style

Another new sector labyrinth in concentric style

In the two lower quadrants we have the courses 1-2-3-4-5 and 5-4-3-2-1. These are the above mentioned pathway sequences at the the 7th and 8th places. The upper two sequences (5-2-3-4-1 and 1-4-3-2-5) are again identical to the aforementioned two labyrinths and the one in the previous post.

The quadratic representation shows that it is actually a mixture of serpentine type and meander type (see Related Posts below).

The new sector labyrinth in Roman Style

The new sector labyrinth in Roman Style

Here in Knidos style:

The new sector labyrinth in Knidos style

The new sector labyrinth in Knidos style

Simply put, in only three sector labyrinths can all theoretically possible eight 5 circuit labyrinths be proved.


But it is also possible to move the “upper” pathways down, so that again arise new display options.
Then you can swap the right and left “lower” quadrants.
Or mirror everything and create right-handed labyrinths.

Here are two examples:

Even one more new sector labyrinth in round shape

Even one more new sector labyrinth in round shape

Another new sector labyrinth in Knidos style

Another new sector labyrinth in Knidos style

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