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

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.

Related Posts

How to make a Wunderkreis or a Baltic Wheel

The Wunderkreis and the Baltic Wheel are compound labyrinths which are constructed from curves around different centres. The two lower turning points are proper for the “labyrinthine” circuits, those in the middle for the double spiral.

A Baltic wheel has a bigger, empty center and a short second exit. This is already a double spiral, yet without more twists. Both accesses are normally separated by an own intermediate piece, a sort of shoehorn.

The pattern for the layout is the same one for both labyrinth types. The tool to produce the layout is also the same. The number of the circuits in all can be different, nevertheless.

Here it is only about the method. The geometrically correct construction is another thing again. There are already several posts in this blog about that.

There is no seed pattern like we have it for the well-known classical labyrinth. However, there is a basically very simple method to draw such a labyrinth or to lay it directly with stones or to scratch it in the sand.

A step-by-step instruction should show it. The boundary lines of the labyrinth are drawn, the path runs between the lines.

Step 1

Step 1

Step 1: I draw half a curve upwards, from the left to the right.

Step 2

Step 2

Step 2: I jump a little bit to the left, make a curve downwards to the left, walk round the first curve and land to the right of the preceding curve.
This would already be the center of the Baltic Wheel or the middle of the smallest possible Wunderkreis.

Step 3

Step 3

Step 3: Nevertheless, the double spiral should become bigger. Hence, I jump again a little bit to the left at the end of the first curve in green, make an other curve downwards to the left and walk again round the preceding curves.
Thus I could continue any desired. There must be left on the right side, however, always two free curve ends. With that the double spiral would be finished inside the Wunderkreis.

Step 4

Step 4

Step 4: Now I must add at least three semi-circular curves round the previous lines.
If I want to have a bigger labyrinth, I can add more lines in pairs. There must however be an odd number of curves.
In our example we now have on the left side three free line ends, and on the right side five.

Step 5

Step 5

Step 5: Now I connect on every side the innermost and the outmost lying free line in such a manner that in between an access is possible. This is to be continued (here only on the right side) so long as on every side only one single line end is left.

Step 6

Step 6

Step 6: The both on every side lying free line ends are extended forwards. They represent the both lower turning points.
The labyrinth is finished.

Finally we will check out if the drawing is correct. We go in between the lines, turn to the right or to the left and must come again to the starting point. If not, something must be wrong.

Best try it out yourself, with a pencil on a sheet of paper. Wishing you success.

Related Posts

How to simply make bigger and smaller Labyrinths, Part 2

In part 1 (see Related Post below) about the simplified seed pattern I only have spoken of the enlargement of labyrinths.

The seed pattern

But of course the number of circuits also can be reduced by this way. This is possible for all labyrinths built from this seed pattern, as well as for all containing this pattern. I would like to call them compounded labyrinths.

For me this are the Indian Labyrinth, the Baltic Wheel and the Wunderkreis. They all have only two turning points, however, the middle is formed in each case differently.
The Indian Labyrinth (Chakra Vyuha) contains a spiral, the Baltic Wheel has a big empty middle and a second access, the Wunderkreis contains a double spiral and also has the second access.

Here the Indian Labyrinth which can be generated through a seed pattern contained in a triangle:

The Indian Labyrinth

The Indian Labyrinth

The Indian Labyrinth with two more circuits:

The enlarged Indian Labyrinth

The enlarged Indian Labyrinth

Here the Baltic Wheel. The middle section is constructed in a special way. But the circuits round the two turning points can be increased or decreased in pairs.

The Baltic Wheel

The Baltic Wheel

The Baltic Wheel with two less circuits:

The downscaled Baltic Wheel

The downscaled Baltic Wheel

The Wunderkreis has a double spiral in the middle section. The double spiral can have more or less windings (not shown here). But the typically “labyrinthine” circuits round the two turning points can be influenced as mentioned above.

The Wunderkreis

The Wunderkreis

The Wunderkreis with two less circuits:

The downscaled Wunderkreis

The downscaled Wunderkreis

In the quoted statements I would like to show that there is a “technology” through that one can influence the size of a labyrinth.

Related Post

How to Walk the Baltic Wheel in Pairs

This way to walk a labyrinth is known as the Appleton for the Classical labyrinth (read more in Further Links at the bottom of this post). Thereby one can go in pairs in the same direction on lanes next to each other. However, one person goes into the labyrinth and the other outwards. This also functions in groups. However, this is only possible on certain lanes, not on all.

In the Baltic wheel this is quite different. There it is possible on all lanes from the beginning to the end. For there are two ways: One long way to walk in or out, a second short way to do the same.

The beginning

The beginning

The blue ball wants to get into the center of the labyrinth and takes the long way in. The yellow ball takes the short way directly into the center, from where it wants to take the long way out.

Home position

Home position

They stand side by side and walk off together in the same direction. It is also possible that others join them and form a long queue, since there is enough place.

Encounter

Encounter

Arriving at the second turning point there is a special moment: They meet each other and their lanes cross.

Shifting the lane

Shifting the lane

But they don’t change direction. They continue their way.

End position

End position

They have both nearly achieved their aim: The blue ball has arrived at the center. The yellow ball approaches the end of its way.

The end

The end

The blue ball can take the short way out. The yellow ball has arrived the exit. Both have exchanged their places.

The end is the beginning and the beginning is the end.

Further Links

Related Post