# Erwin’s Labyrinths with Triple Barriers

Erwin has already shown labyrinths with two axes and triple barriers in one of his earlier posts (see: related posts, below). Here, I want to use these and examine, whether they can be explained based on my courses and sector patterns and how they are composed. They have an even number of axes, and therefore, only courses AB or CD are applicable. Erwin’s Labyrinths, thus must be composed of combinations of sector patterns A and B or C and D. Let’s try if they can be identified with our sector patterns.

Figure 1 shows the first labyrinth by Erwin. This has a course AB and is composed of two sector patterns that are (horizontally) mirror symmetric to each other.

Also the second labyrinth by Erwin has a course AB and as well is composed of two mirror symmetrical sector patterns.

The third labyrinth by Erwin has a course CD and again is made-up of two mirror symmetric sector patterns. In addition, it is the complement of the second labyrinth.

Erwin’s fourth labyrinth, finally, is complementary to the first. Thus it has also a course CD and is made-up of mirror symmetric sector patterns as well.

All four labyrinths by Erwin, thus, are self-transnpose. The first and second labyrinth are two out of 16 possible combinations for the course AB, the third and fourth two out of 16 possible courses CD.

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# The Complementary (transposed) Classical 7 Circuit Labyrinth in Knidos Style

I described this type in the concentric style in my last post (see related posts below). Today it is about the representation of the transposed labyrinth in Knidos style.

The path sequence is: 5-6-7-4-1-2-3-8. The special thing about it is that one enters the labyrinth on the 5th circuit, and the center on the 3rd. circuit.

And yet this type can be aligned to the central axis. This is only possible by editing in the Knidos style.

I come back to the original labyrinth using the same method that I used to get to the complementary type: I add the difference to the last digit (the goal) to the row of numbers in the path sequence. So:
5-6-7-4-1-2-3-8
3-2-1-4-7-6-5-8
8-8-8-8-8-8-8-8
This is then the original, well-known classical (Cretan) labyrinth.

What does the Knidos style actually mean?
By this I mean, above all, that the labyrinth has a larger center than just the width of a path, that it is as compact as possible and, above all, that it is developed from the path sequence and not from the basic pattern for the boundary lines (the walls). So it is Ariadne’s thread, the path in the labyrinth, that determines the construction. And this must be geometrically correct with constant path widths, elements that are as round as possible and as few “spaces” as possible.

Here in another graphic:

The transposed labyrinth in Knidos style

Here are the drawing instructions for a kind of prototype to be scaled for the axis dimension of 1 m.

The design drawing

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

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# The Complementary Classical 7 Circuit Labyrinth

Andreas has written extensively on complementary (transposed) 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 (transposed) 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 (transposed) 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 (transposed) labyrinth in concentric style

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

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 © Matthias Funke

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

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# How to Make (new) 11 Circuit Labyrinths, Part 3

In the previous articles on this topic, I have already explained the method of the stamp-folding calculation brought into play by Tony Phillips.

Now it should go on here. Namely, it is possible to generate further variants of labyrinths by simply rotating the polygon used.

I take again the net with the polygon from the last post on this topic (part 2).

The net with the polygon

This diagram can be used to create four different labyrinths. Two directly (line 2 and 3), the other two by a simple calculation.

Other constellations can be gained by rotating the network 12 times by 30 degrees. Or in other words, it’s just like changing the clock for the summer or winter time.
Since only interesting labyrinths are of interest here, I omit all positions where the lines would point to the first and / or last circuit. So from the 12 you should not reach the 1 or the 11. Only the “times” are interesting, which point farther away, that is, run more sharply.
That would be in the above net the 1, 5 and 6. So I turn only to these times. In other words, I bring the 1, 5, and 6 into alignment with the 12. I turn the net by 30, 150, and 180 degrees. To rotate is the net with the polygon, the numbers stay in place.

Here’s the first turn:

rotated by 30 degrees

I get four completely different path sequences than in the original above.

The second rotation:

rotated by 150 degrees

I get four new variants again.

The last rotation:

rotated by 180 degrees

Here I just get a different order of the sequences than in the original polygon. So there are no new variants, just another arrangement. This is because the rotation of 180 degrees corresponds to a symmetrical reflection.

It is not always possible to find new variants. With the help of this net I have generated a total of 12 different path sequences for 12 new labyrinths.

The path sequences can be directly converted into a labyrinth drawing.
Here only one (again in concentric style) is to be shown (the 2nd path sequence from the first polygon above):

A new 11 circuit labyrinth

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