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## Variations on the Wunderkreis

In my last posting I had introduced a method to draw the Wunderkreis. Besides, it was always about the boundary lines. However, the path (Ariadne’s thread) in the labyrinth can also be drawn with this method slightly changed then.

And of course numerous variations with differently many circuits can be generated for the double spiral and the labyrinthine windings.

Square Wunderkreis

Here in abstract once again the method:

• I begin in the middle
• Arc upwards from the left to the right, jump to the left, arc downwards
• Path: Arc downwards, immediately following an arc upwards (closed line, like a recumbent “S”)
• Jump to the left, curve upwards around the whole
• Repeat this  as often as desired (on the right side there must always be two free ends which point down)
• Then draw around the whole, beginning on the left, an odd number of curves (at least 3, until as much as you want)
• Path: Extend both most internal lines down (maybe connect them)
• Connect the free line ends on every side in loops
• Boundary lines: Extend both most internal lines on every side inside the innermost loop

Sorry, this was a little longer. Maybe it is easier to understand the text together with the drawings. The different colours should help also. Best you try it yourself.

The labyrinth will be mirrored if one draws the first arc to the other direction.
One recognises the representation of the path by the fact that there are only two, perhaps only one line end (how it is also for the other types of labyrinths). If one sees four free line ends, the boundary lines are shown. Nevertheless, in the Wunderkreis the lines do not overlap as we see that in the classical labyrinth.

I have chosen known Wunderkreise as examples for the simplistic representation of the respective alignments.
In the related posts below you may find them all. As well as the step-by-step instruction.

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or, freely adapted from a song by Herbert Grönemeyer (German musician):

## When is a Labyrinth a Labyrinth?

My researches on Wikipedia about the labyrinth have inspired me once again to try an own definition of the labyrinth. This is my proposal:

The labyrinth is (at first sight) a confusing, nevertheless unique, purposeful, artful and meaningful system of lines. The labyrinth, strictly spoken, leads (as a rule) on an unbranched, winding path to the aim, mostly in the middle. The labyrinth, broadly defined, has a branched system of lines with more options, dead ends and loops and is called a maze. The labyrinth as a metaphor signifies confusing and mostly difficult facts and circumstances.

Knidos Labyrinth

Maze

Simple Labyrinth

Type Baltic Wheel

Type Gossembrot

Type Schwanberg

Calligraphic Labyrinth

Crossing Labyrinth

This is probably too long, sounds to complex and looks, hence, quite labyrinthine. Maybe the first sentence would be enough, because it does not exclude the maze and admits the exceptions.

A labyrinth is not always unbranched and totally without every option. Otherwise, the type Baltic wheel (such as the Rad in der Eilenriede at Hannover) would not be a labyrinth. The aim also is not always the middle, especially the geometrical middle or the centre. The Wunderkreis of Kaufbeuren with branching paths is without a real middle and is rather a passageway labyrinth, hence, very well suitable for pageants.

Also the change of course in the movement belongs not necessarily to the labyrinth, because, otherwise, a 3 circuit labyrinth or some modern forms would not be a labyrinth. One can even accept crossroads, like in the Crossing labyrinth of Alana Forest from Australia, because the alignment is unequivocal. One may neither turn left nor right, but always go straight ahead.

Labyrinths and mazes have a lot in common and are related. In colloquial English, labyrinth is generally synonymous with maze. A maze is also a labyrinth (in the broader sense), but a labyrinth (strictly spoken) is not a maze. Since one cannot get lost in it. But it can be bewildering and irritating (at first sight).
I believe, the confusion also comes along that we speak of the labyrinth in the strict sense from a single path free of crossroads and branches and then we show the boundary lines of the labyrinth. Besides, the information refers to the path, Ariadne’s thread, which lies between the boundary lines and is not visible in this form of expression. Just this happened to me at the beginning of my acquaintance with the labyrinth. Only the second and more exact look makes clear the right correlations.

It is the fascination of the labyrinth that it is an ancient, archaic human symbol to be found in different cultures, religions and time epochs and that is open for many interpretations and approaches. This is why it is also qualified for our current time and world as a universal symbol. However, nobody should claim for himself the interpretational sovereignty.

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## How to build a Labyrinth Type Baltic Wheel

The type Baltic wheel is an own form of a labyrinth, for some strict experts it is even none. Since it often has branching paths and a second one, mainly short path from or to the middle. And often at that an outer path with more choices.
The best historical example is the Rad in der Eilenriede in Hannover (Germany). And the restored Wunderkreis of Kaufbeuren (Germany). Others have not survived and are only known in literature.
There is an affinity with the Indian labyrinth (Chakra Vyuha), because it is based like this on the triangle as a basic pattern.

A Baltic Wheel

Here I present a sort of prototype with a dimension between axes of 1 m which is so rotated that the central axis runs by the middle of the widening in the inner part. The eight circuits are surrounded by an outer ring and embedded in a circle with a total of 22 m for the diameter.

The whole is scaleable, that means the dimensions can be changed proportionally by multiplication with a factor. Every measurement multiplied by say 0.5 generates a labyrinth with a diameter of 11 m and a dimension between axes of 0.5 m and cut in halves all radii.
Best of all one starts in the middle and fixes at first the main axis with the points M1 and AX1. The remaining centres M2 to M4 are defined by intersecting the distances from two different (predetermined) points. M5 lies rectangular to the centre M1.

The salient points

Then the axes of the different limitation lines are specified in their designated area starting from the precedent fixed centres of the circles. The different arcs follow each other freely of crease, because they come together in the common tangent vertically to the centre. This sounds more complicated than it is.

Design drawing

Here all measurements in a design drawing.

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