How to Make a Square Classical 3 Circuit Labyrinth Type Knossos

For this kind of labyrinth there is quite an easy basic pattern: Three dashes and two dots. Just as if it were written in our hand. That is what I say to the kindergarten children with whom I explore the labyrinth.

The seed pattern: 3 dashes, 2 dots

The seed pattern: 3 dashes, 2 dots

With it one can draw round or angular labyrinths, but also a square one.







An other nice exercise (not only) for children) is to lay a square labyrinth with matches, paper clips, drinking straws or similar objects similar in size. The center will be three units big, and with a total of 95 components one can make the labyrinth.

A square match labyrinth

A square match labyrinth

The two dots of the seed pattern are replaced by two elements placed horizontally: The left one below, the right one above the vertically arranged three objects.

The seed pattern

The seed pattern

Then we connect the elements with each other, as we already know it from the classical 7 circuit labyrinth. The distance between the lines corresponds to the length of an element.

Children want to trace the way in the labyrinth over and over again, even walk the path. This just succeeds for a width of 20 cm, however, the straws soon will get out of place.

Thus the desire arise to make something more firm. This can best be realized with adhesive tape on the floor. To get the labyrinth really square and rectangular, we need for that a method and a little scheme.

The drawing

The drawing

First we fix a base line. Then the third corner point should be defined. We intersect the diagonal and the side length of the square, outgoing from one end point of the base line. With the same technique the fourth corner point is build. The four sides of the square and both diagonals must have the correct length. So we have produced a figure at right angles.
Then best of all one fixes the end points of the inner lines with the help of the diagonals. After that one connects point for point and will get right-angled lines. The diagonal measurements should better be made by adults, the connection of the points could again be made by the children.

The drawing is designed as a prototype for a unit of 1 m. All specified dimensions are scaleable, so they can be used for labyrinths in different dimensions. For the above shown blue labyrinth all dimensions has been multiplied by the factor 0.21. This proves a path width of nearly 21 cm, an edge length of 1.89 m for the labyrinth, and a total of about 20 m for the lines (adhesive tape).

Here you may see, print, save or copy the PDF file of the drawing

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Labyrinth Movement: Wandering in Meanders towards the Middle

The movement figure in a labyrinth is most essential. For me the meander is the most typical movement pattern. The way through the labyrinth is expressed directly by it.

In this post I try to develop different labyrinth types only with this movement pattern. I will not do it from the seed pattern, but directly from the path sequence (cicuit sequence).

The simplest labyrinth has 3 circuits, and appeared first on a coin from Knossos. This is why Andreas calls this the type Knossos. It is made from one meander and has two turning points (beginning and/or end of the walls). The seed pattern for this labyrinth is very simple: Three lines and two dots.

All examples have a square shape with the same width for the walls and the path(Ariadne’s thread). However, they could be as well round or polygonal. The shape plays no role. The movement figure is crucial.
The seed pattern (in blue) is inserted afterwards in the following examples.

The classical 3 circuit labyrinth

The square classical 3 circuit labyrinth type Knossos

There is still an other  3 circuit labyrinth which can be derived from the diminished seed pattern of the classical 7 circuit labyrinth. Nevertheless, it has the path sequence 1-2-3-4 and does not come up as a historical specimen.

In the type Knossos the path sequence is: 3-2-1-4, this is quite an other rhythm. That has to do with the meander.
I would like to stay at this this movement pattern, and continue with it.

Interim result: The 7 circuit classical labyrinth (sometimes called the Cretan type). This is the oldest historically provable labyrinth type which has presumably been developed from the seed pattern for the walls. It is build from two meanders, connected with a additional path. It has four turning points.

The classical 7 circuit labyrinth

The square classical 7 circuit labyrinth

Now we proceed with an other round, and will get with 11 circuits, 6 turning points and 3 meanders the Labyrinth type Otfrid. Here it is square, the “originals” in the historical manuscripts are all round.

The classical 11 circuit labyrinth

The square classical 11 circuit labyrinth type Otfrid

Meanwhile the course of action might be clear: With every new round, we will have four circuits, one meander and two turning points more.

Here the next example:

The classical 15 circuit labyrinth

The square classical 15 circuit labyrinth (new type)

The displayed example is not known as a historical labyrinth. Although there are other 15 circuit labyrinths. Nevertheless, they look different. Since they have been developed from the well-known seed pattern by adding more angles. We find them among the Scandinavian Troy Towns. Andreas calls the 15 circuit Labyrinth type Tibble.

There exist also 11 circuit labyrinths which have been developed from the enlarged seed pattern. Andreas is naming them type Hesselager.

I design the different labyrinth figures out of another idea: By continuing the typical movement of the meander. Only three examples of the so developed labyrinths match with the historical labyrinths which probably have been generated from the seed pattern. So still nobody has presumably had up to now this thought. One can explain with it the labyrinth figure in a new way, and, by the way, create new types.

The next example in this series is a 19 circuit labyrinth:

The classical 19 circuit labyrinth

The square classical 19 circuit labyrinth (new type)

It is a labyrinth with 19 circuits, 5 meanders, and 10 turning points.

One could continue in this style and develop more and more extensive labyrinths. Who like to do that, can do it for oneself.

With this method one can quite simply explain how to draw a labyrinth. Besides, only the paths, Ariadne’ thread, is drawn. Not the walls. If I speak of lines here, the circuits (the path axis) are meant.
Here an example from a kindergarten child:

An 11 circuit classical labyrinth

An 11 circuit classical labyrinth (type Otfrid)

And here the final work of a kindergarten project on the subject labyrinth. Every child has drawn “his” line in this 19 circuit labyrinth.

A 19 circuit labyrinth

A 19 circuit labyrinth (new type)

The next is a personal “attempt to set up a record”. I have stopped at 23 circuits. However, it would be easy to continue. Maybe you try it yourself?

A 23 circuit labyrinth

A 23 circuit labyrinth (new type)

Now I would like to explain here once again the principle. Your best bed would be to reproduce it for yourself on a sheet of paper. Once one knows how to do it, it is quite easy. At the end everybody should be able to draw Ariadne’s thread for the classical 7 circuit labyrinth by heart and in one go.

I would like to describe the movement pattern very simply, possibly in such a way: I encircle the center by moving to the other side. There I turn outwardly and return in parallel equidistant with the just drawn line back to the beginning side. There I repeat this movement: turning outwardly and tracing back to the previous side. There I turn between the up to now drawn lines into the center. The 3 circuit labyrinth would be finished.
However, I can continue instead and change once again to the other side by following the last drawn line. There the process recurs: Again encircling the center by moving to the other side (thereby leaving enough place for two later lines), then turning outwardly and returing back, and repeating the same. Then to the middle and so on.

It is important to remember that the first drawn line forms the third circuit. This means, I must leave enough place for two more lines, which are drawn later. Namely the second  and the first circuit, which are drawn as the second and the third line. This sounds complex, it is maybe also. However, if one has got the hang of it, it is quite easy.

The first 5 lines (circuits) for a square 11 circuit labyrinth

The first 5 lines (circuits) for a square 11 circuit labyrinth

The next 6 lines (circuits) for a square 11 circuit labyrinth

The next 6 lines (circuits) for a square 11 circuit labyrinth

The direction of movement in the previous examples was from the outside inwards. Thereby I can choose any form, a square, a rectangle, a polygon or a circle. I can make angular lines or rounded ones. If I am in the middle, I have finished.

But easily conceivably would be the reverse movement: From the inside outwardly. Then I would have theoretically no more limitation and could make on and on. A change of thinking for the movement would be required also. Best try it yourself.

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The Cretan at the Crossing Point

The Cretan labyrinth is related to other historical labyrinths in two manners. The easiest way to show this is to compare the seed patterns for the Ariadne’s Thread (see related posts below) of these labyrinths. A first line leads from the Knossos- to the Otfrid-labyrinth. For reasons of space, I arrange this in horizontal order and therefore refer to it as the horizontal line. The other (vertical) line leads from the Löwenstein 3- to the Tibble-labyrinth. The first labyrinth in either line is one of the only two existing alternating one-arm labyrinths with 3 circuits.

  1 / 1                             Löwenstein 3                            1 / 3
  Knossos                              Cretan                              Otfrid
  3 / 1                              Hesselager                            3 / 3
  4 / 1                               Tibble                                4 / 3

The labyrinths of the horizontal line contain exclusively the single double-spiral like meander (Erwin’s type 4 meander, see related posts below). However, they are made up of a varying number, i.e. 1, 2 or 3 of such meanders. Their seed patterns are composed of a varying number of similar segments. A segment consists of two nested arcs.

  • The Knossos-type labyrinth contains one meander. The seed pattern of this labyrinth is made up of two segments. This pair of horizontally aligned segments complete to the meander in the labyrinth.

  • The Cretan consists of two meanders that are connected by a circuit between them. The seed pattern is made up of two pairs of segments aligned vertically.

  • Finally the Otfrid-type labyrinth is made up of three meanders that are connected by circuits between them. The seed pattern consists of three vertically ordered pairs of segments.

All labyrinths of the vertical line consist of two similar figures that are connected with a circuit between them. They all have a seed pattern made up of four similar quadrants. But the seed patterns differ with respect to the shapes of the quadrants.

  • The Löwenstein 3-type labyrinth consists of 2 serpentines. This is reflected in the seed pattern by the four single arcs.

  • The Cretan is composed of 2 single double-spiral like meanders (type 4 meander). The quadrants of the seed pattern of this labyrinth consist of two nested arcs.

  • The Hesselager type labyrinth is made up of 2 two-fold (type 6) meanders. The quadrants in its seed pattern are made up of three nested arcs.

  • Finally, the Tibble-type labyrinth consists of 2 three-fold (type 8) meanders, the quadrants of its seed pattern are made-up of four nested arcs.

The images above are arranged in the form of a table or matrix with 4 rows, 3 columns and 12 fields (frames). Six of these frames contain seed patterns directly related to the Cretan, the others are still void. The relationships of the horizontal and vertical line can also be formulated as follows:

  • Progressing (horizontally) one column to the right will increase the number of meanders by one.
  • Progressing (vertically) one row downwards will increase the depth of the meander by two. The depth of a meander corresponds exactly with it’s type number – a type 4 meander has depth 4, a type 6 meander depth 6 a.s.f.

With this information we are able to add the missing seed patterns and the corresponding labyrinths. By doing so we will encounter two other historical labyrinths and one figure that is no labyrinth. Of course it is also possible to add more rows or columns to the table and to fill the new frames with the corresponding seed patterns. All figures generated this way are self-dual. The figures of the first row are, in the terminology of Tony Phillips, uninteresting, all other figures are very interesting labyrinths (see related posts below).

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The Hexagonal Classical 3 Circuit Labyrinth

We still had the whole labyrinth inside the Flower of Life on this blog (see related posts below). However, the middle was as small (one path width) as we know that from the classical 7 circuit labyrinth.

How does it look now if one makes the middle bigger and maintains, besides, the hexagon?

The 3 circuit labyrinth in hexagonal shape

The 3 circuit labyrinth in hexagonal shape

The paths are still defined by the well-known path sequence 3-2-1-4.
Also the classical 7 circuit labyrinth can be brought into hexagonal form and will preserve its typical path sequence 3-2-1-4-7-6-5-8.

The 7 circuit labyrinth in hexagonal shape

The 7 circuit labyrinth in hexagonal shape

The different labyrinth types do not depend from the external form.
Another type ordinarily is got through a changed path sequence.

Thus can be inserted, for example, within our 3 circuit labyrinth at two places “barriers” which cause another alignment. Thereby the firstly one axis labyrinth will change to a 3 axis labyrinth.

A hexagonal 3-circuit 3-axle labyrinth

A hexagonal 3-circuit 3-axle labyrinth

The alignment is a little more complicated and the path sequence is: 3-2-1-2-3-2-1-4. Three sectors are walked one after the other like in a Roman labyrinth. First I turn to the middle, then outwardly, then again to the middle, again outwardly and from very outside, finally, I reach the center.

I can also turn the labyrinth and take a horizontal edge as a base. Then it looks as follows, drawn inside the Flower of Life:

The switched hexagonal labyrinth inside the Flower of Life

The switched hexagonal labyrinth inside the Flower of Life

This does not arise compelling from the geometry of the Flower of Life, hence, is a further development or a playful modification.

I could imagine this quite well as a labyrinth from paving tiles. Who builds one?

Nice honeycomb patterns can be generated from the hexagon. The bees make this; why could we not have a labyrinthine honeycomb pattern?
The hexagon can be mirrored and switched (six times) and combined in different patterns.

Labyrinthine honeycombs

Labyrinthine honeycombs

If one makes now a wallpaper, or wall tiles, or flagstones from it, the entrances will get “enframed”. But, nevertheless, within each single honeycomb the unequivocal way of the labyrinth (Ariadne’s thread) can be seen.
Otherwise, even irritating visual perceptions are possible. Since the hexagon contains also the edges of a cube.

Labyrinthine honeycomb pattern

Labyrinthine honeycomb pattern

To be continued …

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