The Doctopus Labyrinth

Gundula Thormaehlen-Friedman once again was creative. And so this new double octopus labyrinth was created. I derive the name from the core of her idea, the double eight semicircles in the middle of the labyrinth. These also form the seed pattern for Ariadne’s thread (see related articles below).
The free ends of these 16 semicircles can be connected to one another in different ways. So the well-known Classical 7 circuit labyrinth appears, or other variants, such as e.g. the snail shell labyrinth (see also below).

Ariadne's thread in the Doctopus Labyrinth

Ariadne’s thread in the Doctopus Labyrinth

What is so special about this labyrinth? A lot.
For a better explanation, a drawing of the thread follows in a simplified form with some construction elements.

The construction elements

The construction elements

The labyrinth actually spans a sphere. However, it is opened and therefore shows two poles. It is reminiscent of the globe. The vertical axis, like the earth’s axis, is inclined. The thread is intersected on the horizontal axis (equator), but at the same time also linked here. This is the axis crossing in horizontal form.
The beginning and the end are in the middle, not outside and inside as usually.
The access is, as it were, on another level (like a tunnel or a bridge), so it looks two-dimensional (see the post about the outback at the bottom). This also turns it into a walk through labyrinth.
However, if I follow the path sequence, I end up with 0-3-2-1- | -4-7-6-5-8. And that’s the well-known Classical 7 circuit labyrinth.
The thread can also be numbered differently. Then I will get a different path sequence, e.g. two linked labyrinths, a 3 circuit and a 4 circuit labyrinth.

Gundula and her daughter Dara Friedman were able to realize their ideas in a project in Florida. A versatile labyrinth was created there. A relationship and encounter labyrinth was born.

The Doctopus Labyrinth, photo: © Dara Friedman

The Doctopus Labyrinth, photo: © Dara Friedman

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How to Draw a Man-in-the-Maze Labyrinth / 11

Completion of the Seed Pattern

Two more steps are still needed in order to bring the Chartres-type labyrinth into the Man-in-the-Maze style. First, the seed pattern has to be completed.

We already have the seed pattern for the walls delimiting the pathway, but still without the pieces of the pathway that traverse the axes. These are still represented as pieces of the Ariadne’s Thread (fig. 1).

Figure 1. Seed Pattern and Pieces of Path Traversing the Axes

 

The labyrinth should be represented entirely by the walls delimiting the pathway. For this, the walls around the pieces of the path traversing the axes have to be completed (fig. 2).

Figure 2. Completion of the Walls Delimiting the Pathway – 1

We begin from the outside to the inside and first draw the walls around the outermost of these pieces of the pathway.

As a next step we add the walls delimiting the next inner pieces of the pathway (fig. 3).

Figure 3. Completion of the Walls Delimiting the Pathway – 2

As one can see, in each step, for each piece of the path, 2 or 4 for spokes have to be prolonged inwards, which are then connected with an arc of a circle.

And so we continue until all pieces of the path traversing the axes are enveloped by walls delimiting them (fig. 4).

Figure 4. The Final Seed Pattern for the Walls Delimiting the Pathway

This results in the complete seed pattern for the walls delimiting the pathway. In the center of the seed pattern and where the path traverses the axes there exist areas that are not accessible. This is quite analogue with the seed patterns in alternating labyrinths in the MiM-style, in which the center is not accessible either.

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How to make a Classical (Minoan) Labyrinth from a Medieval Labyrinth, Part 3

Quite simply: By leaving out the barriers in the minor axes. I have already tried this with the Chartres labyrinth some years ago. And in the last both posts on this subject with the types Auxerre and Reims. You can read about that in the related posts below.

Today I repeat this for the Chartres labyrinth. Here the original in essential form, in a concentric style.

The Chartres labyrinth

The Chartres labyrinth

The original with all lines and the path in the labyrinth, Ariadne’s thread. The lunations and the six petals in the middle belong to the style Chartres and are left out here.

Now without the barriers in the minor axes.

The Chartres labyrinth without the barriers

The Chartres labyrinth without the barriers

All circuits can be included in the labyrinth originating now, differently from the types Auxerre and Reims. The path sequence is: 5-4-3-2-1-6-11-10-9-8-7-12. We have eight turning points with stacked circuits. It is self-dual. That means that the way out has the same rhythm as the way in.

But this 11 circuit labyrinth is quite different from the more known 11 circuit labyrinth, that can be generated from the enlarged seed  pattern.
Since this looks thus:

The 11 circuit labyrinth made from the seed pattern

The 11 circuit labyrinth made from the seed pattern

The path sequence here is: 5-2-3-4-1-6-11-8-9-10-7-12. We have got four turning points with embedded circuits. It is developed from quite another construction principle than the Chartres labyrinth. However, it is self-dual.


Now we turn to the complementary labyrinth.

The complementary labyrinth is generated by mirroring the original. Then thus it looks:

The complementary Chartres labyrinth

The complementary Chartres labyrinth

The entry into the labyrinth happens on the 7th circuit, the center is reached from the 5th circuit. The barriers are differently arranged in the right and left axes, the upper ones remain. It is self-dual.

Without the barriers it looks thus:

The complementary Chartres labyrinth without the barriers

The complementary Chartres labyrinth without the barriers

The transformation again works, as it does for the original. The path sequence is: 7-8-9-10-11-6-1-2-3-4-5-12. Also this labyrinth is self-dual.

We confront it with the complementary labyrinth, generated from the seed pattern.

The complementary 11 circuit labyrinth made from the seed pattern

The complementary 11 circuit labyrinth made from the seed pattern

The path sequence on this is: 7-10-9-8-11-6-1-4-3-2-5-12.
Contrarily to the original this type did not show up historically.

So we have created two completely new 11 circuit labyrinths from the Chartres labyrinth, which look different than the 11 circuit labyrinths that can be developed from the seed pattern.

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How to Draw a Man-in-the-Maze Labyrinth / 10

Traversing the Axes

In alternating labyrinths with multiple arms the pathway does not traverse the main axis. However, it must traverse each side-arm (see below: related posts 1). How then have the axes to be traversed in the MiM-style? Let me first remember that I have already transformed a non-alternating labyrinth with one arm into the MiM-style (see related posts 2). From this it can be seen what happens when the pathway traverses the axis (figure 1).

Figure 1. Labyrinth of the St. Gallen Type in the MiM-Style

At the places where the pathway traverses the axis, the innermost circle is interrupted. The pieces of the pathway traversing the axes, and only these, in the MiM-style pass through the center of the seed pattern. In all alternating one-arm labyrinths the innermost circle is closed. The center of the labyrinth lies outside of it in any case.

Now for the Chartres type labyrinth in the MiM-style, in each side-arm several pieces of the pathway have to be passed through the middle. From the seed patterns it can clearly be seen, where the side-arms are traversed. These are the gaps between the pieces of arcs where the innermost circle is interrupted. Let us have a look at the firs side-arm in detail (figure 2). The seed pattern of this side-arm lies in west quadrant (highlighted in black).

Figure 2. The Seed Pattern of the First Side-arm

The purpose is to transform the pieces traversing this side-arm into the MiM-style (figure 3).

Figure 3. The Pieces of the Path Traversing the Axis

As everybody knows, the pathway in the Chartres type labyrinth first leads along the main axis to the 5. circuit, makes a turn at the first side-arm, returns to the main axis on circuit 6 and from there reaches the innermost 11th circuit. On this circuit it follows half the arc of a circle whilst it traverses the first side-arm. Then it makes a turn at the second side-arm. From there it returns on the 10th circuit to the main axis whilst passing the first side-arm again. The pathway also traverses the first side-arm on the 7th, 4th and 1st circuit. The pieces of the pathway on the outer circuits enclose those on more inner circuits and outermost piece of the pathway on circuit 1 encloses all others.

Figure 4 shows what happens with the pieces of the pathway traversing the axis (colored in red, the color of the Ariadne’s Thread), when the side-arm is transformed from the concentric into the MiM-style.

Figure 4. Transformation from the Concentric into the MiM-style

The left image shows the side-arm split and slightly opened. The course of the pieces of the path is still quite similar as in the base case from bottom up or top down. However, all pieces of the pathway bend to the opposite direction. In the central image the original course is hardly recognizable any more. Both halves of the side-arm are widely opened. The pieces of the path sidewards come in to the one half and leave from the other half of the side-arm. Between the two halves of the side-arm their course is in vertical direction. The pieces of the pathway on inner circuits enclose the pieces more outwards. The innermost piece on circuit 11 encloses all others. Next, there is only a slight change from this to the right image. All the pieces of the pathway and the seed pattern are transformed into a shape so that they lie between (pieces of pathway = pieces of the Ariadne’s Thread) and on (seed pattern for the walls delimiting the pathway) the spokes and circles of the MiM-auxiliary figure.

Figure 5 shows all three side-arms with all pieces of the pathway traversing the arms in the MiM-style.

Figure 5. All Traverses of Axes

The west and east side-arm have five each, the north side-arm has three pieces of the path traversing the axis. Therefore in the center of the MiM-auxiliary figure additional auxiliary circles are needed to capture the paths traversing the axes. For this, five auxiliary circles are required. And also the spokes have to be prolonged further to the interior. This is because the walls delimiting the pathway (black) all come to lie on the auxiliary circles and spokes. Near the center the distances between the spokes are continually narrowed. Therefore the innermost auxiliary circle must have a certain minimum radius for the walls and the pathways not to overlap each other.

Now we have all elements together we need to finalize the Chartres type labyrinth in the MiM-style.

Related posts:

  1. How to Draw a Man-in-the-Maze Labyrinth / 9
  2. How to Draw a Man-in-the-Maze Labyrinth / 6