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Welcome to the Labyrinth

The topic of this blog is the labyrinth. Under nearly all aspects, I would like to arouse your interest on the fascinating lines and the meaning of this old object. Being an old surveyor I put my focus on the geometrical shape.
A new post should be published about twice a month. Meanwhile I am accompanied by Andreas Frei as coauthor.

Contents

In a blog the single posts (articles) are disposed in reverse order: the latest posts first, the older ones following. The display of the content is thus different from a website where it is always permanent.

Anyone who is looking for something special about labyrinths or just wants to know what can be found on this blog, maybe would like to have an overview.

I can provide this now and offer it as an own page titled Contents.

The register with the table of Contents is on top of the blog under the header image next to About us.

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For a better view

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Rights of use

Most of the pictures and graphics were created by Andreas Frei and me (Erwin Reißmann), unless stated otherwise, and are provided under license CC BY-NC-SA 4.0.

The Complementary Classical 7 Circuit Labyrinth

Andreas has written extensively on complementary labyrinths. See related posts below.

I want to go into this type again today: The complementary to the classical labyrinth. Because it is a very interesting labyrinth and as such it deserves a wider distribution among the newly created labyrinths. In addition, it is one of the few self-dual labyrinths.

Here the pattern in diagram form with the circuit sequence:

The pattern of the complementary labyrinth

The pattern of the complementary labyrinth

So what’s so special about this kind of labyrinth? The entrance is on the 5th circuit, then we move quickly towards the center and circle around it. From there it goes all the way out to the 1st circuit and from there towards the middle and finally to the center from the 3rd circuit.
There is, as it were, a much greater dynamic in the routing than in other types. This is expressed in the axial shift, the jumps from circuit to circuit: 5f (forwards) – 1f – 1f – 3b (backwards) – 3b – 1f – 1f – 5f.

Here are some examples in different styles:

The complementary labyrinth in different styles

The complementary labyrinth in different styles

Upper left in the Cretan style, next to it concentrically, below in rectangular and square form. They look different, but they all have the same path sequence, so they are of the same type.

Again, more precisely and in more detail: the concentric variant:

The complementary labyrinth in concentric style

The complementary labyrinth in concentric style

In addition, a construction drawing for a kind of prototype with 1 m axis dimension.

The design drawing

The design drawing

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

In the meantime, some brave labyrinth enthusiasts have laid such a labyrinth out of stones near Duisburg at Rhine km 768. Thanks for that.

The labyrinth at Rhine km 768, photo © Volker Bahr

The labyrinth at Rhine km 768, photo © Volker Bahr

The labyrinth at Rhine km 768, photo © Volker Bahr

The labyrinth at Rhine km 768, photo © Volker Bahr

The labyrinth at Rhine km 768, photo © Matthias Funke

The labyrinth at Rhine km 768, photo © Matthias Funke

Let’s hope that this example will take on and that more labyrinths of this type will be built soon.

Related Posts

How to Generate the Seven Times Seven Labyrinth

For New Year I have presented the Seven Times Seven labyrinth (see: related posts 1, below). Erwin has immediately commented and noticed the similarity with the type Gossembrot 51 r. This is correct. I wanted to develop a self-dual labyrinth based on this type. And I wanted to preserve the typical characteristics of the course of the pathway. Typical for Gossembrot’s labyrinth are not only the double-barriers, but also the manner in which the path is directed through all segments. It is not a sector labyrinth, but rather in about the opposite of that.

In figure 1, I show the pattern of the Gossembrot 51 r type labyrinth. This serves as the starting point (a) and is presented in grey. I have already described earlier, what characterizes the course of the pathway (related posts 2). This happens in segments III to V. Another speciality is the meander in segment II. This meander lies on the circuits 2 – 6. So there is one more circuit each outside and inside of the meander.
First, I isolate the segment that contains the meander (b). The meander itself is self-dual. And, since there are added one more circuit each, at the outside and inside, the whole figure (b) is self-dual too. To this figure are attached on the right side segments III – V. These contain the typical course of the pathway by Gossembrot. From the fact, that segment II is self-dual, it also follows that one of its sides can be connected with a figure that is the dual to the figure connected with its other side. In a second step, therefore, I pick out the figure in segments III – V and place it to the right side of segment II. Figure (c), thus, shows nothing else than segment II not connected with segments III – V of the pattern of Gossembrot 51 r.

Figure 1. Preparation

This figure (c) forms the basis for the generation of the Seven Times Seven labyrinth, or of it’s pattern respectively. The process is shown in fig. 2. Here we begin in the third row with the figures colored in grey (c). In a third step, the figure from segments III – V is now duplicated (d). This duplicate is then rotated by 180 degrees in a fourth step. This produces the dual figure of it (e). Then we shift it downwards and can see: it can be connected to the left side of the figure with the meander from segment II (f). Now we only have to really connect these elements with each other and by this obtain in figure (g) the pattern of the Seven Times Seven labyrinth.
This whole pattern is self-dual. The number of segments has increased from the five segments of the labyrinth type Gossembrot 51r to new seven segments. The dual of Gossembrot’s segments III – V covers the new segments I – III, the meander with its additional circuits inside and outside follows in central segment IV, and Gossembrot’s original segments III – V are here shifted to segments V – VII.

Figure 2. Generation of the Pattern

Figure 3 shows the labyrinth in the basic form without the heptagram in the center and without the heptagon at the periphery. These are add-ons and have to be attributed to the style, rather than to the type of labyrinth.

Figure 3. The Labyrinth in Base Form


A very well balanced labyrinth. The main axis looks the same as in the basic type. Opposite to the main axis, in the central segment IV, lies the meander. In three segments before and after the meander, the typical course of the pathway can be found. The path proceeds in wrapping or wrapped curve through all segments, thereby passing the meander and arrives in a backward movement through sectors VII – V in sector IV, through which it continues as meander, then continues its backward movement through sectors III – I, from where it leads in forward direction through all segments to the center.

Related posts:

  1. Labyrinth for the New Year 2020
  2. Sigmund Gossembrot / 2

How to Make a 6 Circuit Wedding Labyrinth

I recently featured a 4 circuit wedding labyrinth (see related posts below). I also described the requirements such a labyrinth would have to meet.
Today I would like to introduce a 6 circuit labyrinth. It’s already known as a type. Here it is intended to be used as a two-part and open labyrinth.

In concentric shape

In concentric shape

The labyrinth is entered on the 3rd circuit, the center from the 4th circuit.
As a result, the bridal couple walk side by side on the first and the last part of the way.
The bridal guests can line up outside and inside around the labyrinth. This is a good way to straighten and loosen up the ceremony.

Here the labyrinth in the compact Knidos style.

The 6 circuit labyrinth in Knidos style

The 6 circuit labyrinth in Knidos styleThe three “empty spaces” in the labyrinth can be used for decorations of all kinds.

Here is a kind of prototype with an axis dimension of 1 m. This makes it easy to scale.

The layout drawing

The layout drawing

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

Related Posts

Sector Labyrinths with Double-barriers – Summary

Today I want to come to an end for the moment. I have begun with 4 arm labyrinths with double-barriers the same as were used by Gossembrot (see: related posts 3). Later I have referred to these as real double-barriers. Subsequent to a comment by Erwin I have also considered labyrinths with pseudo double-barriers. There already exists a historical type of such a labyrinth, the Avenches type. Real and pseudo double-barriers can also appear in combinations in the same labyrinth (related posts 2).

Labyrinths with double-barriers and five circuits must be sector labyrinths. Double-barriers can only appear in side arms. Therefore, a labyrinth with a double-barrier must have at least 2 arms. For each number of 2, 3, 4 and 5 arms there are always 8 different labyrinths using real double-barriers.

This suggests the conclusion that the number of different labyrinths with only real double-barriers is independent of the number of arms. It depends solely from the four sector patterns that can be placed in the first and the four that can be placed in the last sector. Two of the four sector patterns for the first sector are connected on the outermost, two on the innermost circuit with the following sector. Likewise, two of the four sector patterns each for the last sector are connected on the outermost or the innermost circuit respectively with the sector before them. This results in the 8 different labyrinths with tow arms and one double-barrier (related posts 1).

The number of arms can be only increased by inserting additional sectors between those two sectors next to the main axis. In these sectors between the first and the last sector only sector patterns no. 3 or no. 8 can be placed. And, in addition, these must be ordered in alternating order. Therefore, for the sectors between the first and the last sector, in any case, only one interface is available. Two complementary arrangements are possible for any number of arms. One of them begins with sector pattern no. 3, the other with sector pattern no. 8. For each of these arrangements, four different patterns can be generated by connecting them with the appropriate sector patterns of the first and of the last sector.

Thus, there are 8 different labyrinths using exclusively real double-barriers for any number of more than one arms. For each of these labyrinths, a tree diagram can be constructed. We have shown this with the example of labyrinth D (related posts 2). The tree diagram contains patterns for labyrinths with only real, only pseudo and for mixed double-barriers. The tree diagram has shown us, that there are the same number of patterns with exclusively pseudo as with exclusively real double-barriers. The uppermost branch of a tree diagram is made-up of the patterns with only real, the lowermost branch of those with only pseudo double-barriers. This too is true independent of the number of arms.

However, this is not valid for the number of labyrinths with combined double-barriers. This number rapidly increases as the number of arms increases. So, in two arm labyrinths there are only either 8 with a real or 8 with a pseudo double-barrier, but none with combined double-barriers, as these labyrinths can have only one double-barrier. In 3 arm labyrinths, again there are 8 with only real, 8 with only pseudo and, in addition, 16 with combined double-barriers. In 4 arm labyrinths we have seen, that there are 48 labyrinths with combined double-barriers. Finally in 5 arm labyrinths the number of labyrinths with combined double-barriers increases to 112 etc.

Related posts:

  1. The Two Arm Labyrinths with a real Double Barrier and 5 Circuits
  2. The Labyrinths With Real or Pseudo Double-barriers, 4 Arms and 5 Circuits
  3. The Labyrinths with 3 Double-barriers, 4 Arms, and 5 Circuits