Feeds:
Posts
Comments

Posts Tagged ‘construction’

In the meantime, I have developed for myself a method to construct a labyrinth by only using the path sequence. I do not apply the seed pattern to do that.

I would like to show this here for a 7 circuit classical labyrinth with the path sequence  0-3-2-1-4-7-6-5-8. It is from an other shape as the usual classical labyrinth and was to be seen in a previous post.

First I draw freehand the path of the labyrinth (Ariadne’s thread) according to the path sequence. To get an other shape, I cross the main axis with the 4th and the 7th circuit. From the sketch I derive the number of the turning points and the construction lines. Then I count the number of the ways between the central point and the turning points which are also centers in the further construction.

The freehand sketch

The freehand sketch

The broad for the paths and the walls is the same with 1 m, this makes a dimension between axes of 2 m. The diameter of the middle is the fourfold dimension between axes. The lengths of the different construction lines are calculated from this details.
I begin with a horizontal line (M2 – M3) and I fix the central point M1 by applying the two distances from M2 and M3. In the same way the other points are defined. (Fig. 1)

The construction lines

The construction lines

Starting from the center M1 I draw auxiliary circles in an interval  of 1 m from the inner to the external diameter. (Fig. 2)

The auxiliary circles

The auxiliary circles

The lines M1 – M2 and M1 – M3 are extended up to the external diameter, also the lines M2 – M4 and M3 – M5. (Fig. 3) They are limiting the circular arcs.

The external arcs

The external arcs

Then the different curved sections are drawn with the help of the path sequence in the centers M2 to M5.
In fig. 4 this are the semicircles around the turning points of the ways 5/6 in M2 and the ways 6/7 in M3. The construction is made through connection with the end points of the bigger external arcs.
In fig. 5 the curved sections of the remaining external arcs are formed around the centers M2 and M3.
In fig. 6 follows the connection of the ways 1/2 around M4 and the ways 2/3 around M5.
In fig. 7 the open, innermost pieces of the way are connected by strictly watching the path sequence. These are curved sections which joins each other without sharp bends.

The inner arcs

The inner arcs

In fig. 8 I turn all curves and lines around the center M1 in such a way that the entry axis for the middle is strictly vertical.

Fig. 9 shows the completed labyrinth. The paths are highlighted in color. The walls have the same broad and are left white. The left blank fontanel is good to recognise. It has another shape as the usual classical labyrinth. It appears when the paths are drawn in constant width.

The 7 circuit Knidos labyrinth

The 7 circuit Knidos labyrinth

The drawing is rather a sort of model or template. The labyrinth can still have got different shapes, can be angular or completely round, right- or left-handed. The paths and the walls can be of different widths, also the middle can be bigger or smaller. It is only important to maintain the alignment of the labyrinth.

Related Posts

Advertisements

Read Full Post »

To draw the labyrinth from the basic pattern, still fascinates everybody which does it the first time. There is the basic pattern for the boundary lines (the walls) and since 2010 also the basic pattern for the path, Ariadne’s thread.

However, this is not the only possibility. On exploring the meander I have generated labyrinths from different meander combinations, and have found well-known and new types unknown still up to now.
I have seen the meander as a source for the path sequence in the labyrinth. Since a labyrinth is defined above all by its path sequence, even tough not only.

When drawing freehand Ariadne’s thread I have discovered that there are sometimes several possibilities to change the direction of a circuit.

This inspired me to look for other variations for the well-known classical 7 circuit labyrinth with the meanwhile equally well-known path sequence 0-3-2-1-4-7-6-5-8.
And I have found three other labyrinth shapes with the same path sequence.

I have determined the basic pattern contained in it and the angular thread of Ariadne in form of the meander not until the labyrinth construction.

Here at first the familiar classical labyrinth in “pure form”:

The classical 7 circuit labyrinth

The classical 7 circuit labyrinth

The basic pattern for the walls is emphasized in color. Ariadne’s thread in diagram form shows that the path in the labyrinth is composed of two simple meanders (named type 4 by me).
The labyrinth has 7 circuits, four turning points and the path sequence 0-3-2-1-4-7-6-5-8.


In this variation the fourth circuit crosses the main axis and from the same path sequence as in the preceding labyrinth appears a new type:

A 7 circuit classical labyrinth with the 4th circuit crossing the axis

A 7 circuit classical labyrinth with the 4th circuit crossing the axis

The basic pattern is pulled apart and split. Ariadne’s thread is equally pulled apart, but both meander elements are clearly recognizable.
The labyrinth has 7 circuits, four turning points and the path sequence 0-3-2-1-4-7-6-5-8, however, quite an other shape.


Here the 7th circuit crosses the main axis and from the same path sequence a new type is generated:

A 7 circuit classical labyrinth with the 7th circuit crossing the axis

A 7 circuit classical labyrinth with the 7th circuit crossing the axis

The basic pattern is shifted again and split. Ariadne’s thread is changed, recognizable, however, the second element is mirrored.
The labyrinth has 7 circuits, four turning points and the path sequence 0-3-2-1-4-7-6-5-8, however, again quite an other appearance.


Now the 4th and 7th circuit crosses the main axis and from the same path sequence again a new type is produced:

A 7 circuit classical labyrinth with the 4th and the 7th circuit crossing the axis

A 7 circuit classical labyrinth with the 4th and the 7th circuit crossing the axis

The basic pattern is shifted and split. Ariadne’ s thread is changed, however, the two meander elements are recognizable.
The labyrinth has 7 circuits, four turning points and the path sequence 0-3-2-1-4-7-6-5-8, however, again quite an other appearance.

There are for the same path sequence four different shapes. It’s difficulty to name them correctly (and in short terms). Here one sees clearly that the information of the path sequence is not sufficient for the definition of a type.

Now one could ask, why there existed up to now no labyrinths of these types. From the modified basic pattern they are not easily to build, from the meander probably also not.

Considered closely, these three new variations doesn’t look especially nice. The components of square and circle do not make an appearance. The original, oldest and well-known version of the classical labyrinth is well-balanced and harmonious. There’s nothing like the good, old Cretan labyrinth. This shows up once more.

Related Posts

Read Full Post »

After you have seen several times the different seed patterns in the labyrinth, now a common consideration should follow: There is the seed pattern for the walls (limiting lines) and the seed pattern for the path, the so-called Ariadne’s thread.

While I tried to build a geometrically exact labyrinth from the different patterns, it has struck me that both seed patterns are not so different at all. And thus I would like to show both together.

Here first the square which four sides are divided into eight constant parts. In a drawing one can take squared paper and make every side 4 cm long. In  reality this would be four metres and the drawing would be on a scale of 1:100.

The scaled square

The scaled square

The mark and name of the different points already states something about the later use within the construction. “A” is the starting point; “Z” the goal or the centre, at the same time, however, also a centre of different arcs. Hence, marked with a bigger symbol of a circle. As well as the four corner points M1 to M4, also centres of arcs. And at same time delimiters for the walls.
The path axes (Ariadne’s thread) are marked with a small cross and are numbered from 1 to 7. In between are the walls which are marked with small circles.

The angular seed pattern for the walls

The angular seed pattern for the walls

Here the well-known seed pattern with the isosceles cross, the four angles and the four dots.

The round seed pattern for the walls

The round seed pattern for the walls

However, the lines must not be angular, they can also be rounded and then the pattern looks like above.

The seed pattern for Ariadne's thread

The seed pattern for Ariadne's thread

The seed pattern for Ariadne’s thread looks in the limiting square like on top.

The two seed patterns in the square

The two seed patterns in the square

If both patterns are shown together, one recognises the relationship and resemblance between them. And also that the centres of the different arcs are same. No surprise, because the lines are parallel and the red thread is, finally, the middle between the black boundary lines, so to speak the path axis.

Afterwards I would like to point out which arcs are constructed from a total of five centres. There are quarter circles and semicircles which run in each case in different sectors. The order is as you like, since basically it makes no difference which curve is drawn or constructed first. This arises by itself, if one applies the principle for the drawing of a labyrinth properly. As it was described in the older posts on this blog.

Tip: The following, as well as all remaining drawings, can be clicked to enlarge. Then a new window is opened.

The centre M1 top left

The centre M1 top left

The centre M2 bottom left

The centre M2 bottom left

The centre M3 bottom right

The centre M3 bottom right

The centre M4 top right

The centre M4 top right

The centre Z on top

The centre Z on top

The classical seven circuit labyrinth

The classical seven circuit labyrinth

Here the finished labyrinth with the walls in black and Ariadne’s thread in red. It is a classical seven circuit, left handed labyrinth.

Prototype

Prototype

 

If you would like to build such a labyrinth, you will find all specifications and all radii in this design drawing on a scale of 1:100. It is a sort of prototype for a dimension between axes of  1 m and scalable.

Read Full Post »

The labyrinth in its simplest form is one with 3 circuits. For some people it is not a “real” labyrinth because the path is leading directly into the centre without being closer and then farther away from it.
As there is no universally valid definition for the labyrinth, we may nevertheless consider this labyrinth as a real one.

The labyrinth with 3 circuits

The labyrinth with 3 circuits

How do we get one?

The basic pattern to make a 7-circuit classical labyrinth is known, in the meantime, probably by all readers of this blog. (If not, please take a look here.)

No 3-circuit historical labyrinths are known, it is made from a reduction of the basic pattern. If one omits the four angles, only the cross and the four dots are remaining.

The pattern

The pattern

This reminds a little: Dot, dot, comma, dash – smiley face in a flash :-). However, it is really so simple to make a labyrinth, and this is why it is a child’s play to draw one this way.

The first arc

The first arc

The second arc

The second arc

The third arc

The third arc

The fourth arc

The fourth arc

However, there are still other methods to draw the labyrinth: In two lines, from one end of the line to the other end. Try to draw it on a sheet of paper. So often that you can do it by heart.
Tip for right hander: Begin at the left end. Left-handed persons are beginning at the right end. The lines may become crooked.
With two lines

With two lines

An other variation would be to begin in the central intersection point and to draw to all four directions. This has practical meaning if one would build a labyrinth with different material for example.
With four lines

With four lines

The most elegant method is to draw the labyrinth in one line. Therefore we take the path, the famous thread of Ariadne. We can begin on the inside or from the outside.
Ariadne's Thread

Ariadne's Thread

Who realises this by heart, maybe even for the 7-circuit labyrinth, may be called labyrinth expert.

Here a few examples of 3-circuit labyrinths:

Ceramic

Ceramic

Artwork

Artwork

Graphic art

Graphic art

The first picture shows a gem of Alexander Lautenbacher.

The central picture shows the shoe labyrinth from Schwäbisch Hall. The four “shoe lines” are beginning in the central intersection point.

The last picture shows the graphic on the invitation card from the Labyrinth Society for the Gathering this year.

Read Full Post »

The classical labyrinth always was depicted in rectangular shape, just in the oldest representations on coins and engravings.

The classical labyrinth in rectangular shape with small centre

The classical labyrinth in rectangular shape with small centre

Again one recognises very well the basic pattern in a rectangular form. The path sequence also is typical.

The classical labyrinth in rectangular shape with large centre

The classical labyrinth in rectangular shape with large centre

The centre should be bigger than only a path width. Because the square basic pattern was maintained, the centre becomes an irregular, rectangular polygon.
How does one get, however, a completely square labyrinth?
This is only possible if one gives up the basic pattern and makes the centre, e.g., with the 5-fold path width.
Then the labyrinth looks like this:

The classical labyrinth in square shape with large centre

The classical labyrinth in square shape with large centre

The path sequence is preserved, the form has changed. But it remains a classical labyrinth.

Who would like to build one, is invited to see, print, store or copy the layout drawing as PDF file.

Read Full Post »

We already had the classical labyrinth in round form in a preceding post.

If one makes the lines less round around the four points of inflection, this labyrinth shows a certain form of meander. In fact this labyrinth can be developed from two double meanders.

A round classical labyrinth

A round classical labyrinth

How to make a labyrinth with a double meander is shown in this Flash animation on mymaze.

Who would like to build such a labyrinth, is invited to use the following layout drawing.

Here the drawing as PDF-file (in German) to look at, to print or to copy.

Read Full Post »

The preparations for this labyrinth are known. They were object of the previous article with the title: How to build a Knidos Labyrinth with Bark Mulch.

This was as it were the test run or a specimen for the final version.

In the meantime, the meadow had been mowed once again and the bark mulch had disappeared to a great extent. Hence, for the preparation of the construction the lines had to be marked out again. Following the still recommended method the 5 mean points were marked again with iron bars. Beginning from the inside, the limitations of the labyrinth were sprayed on the ground outwardly with white spray paint. A double line was chosen at about 14 cm width. This was the mark for the pits to be dug up with the spade.

Here pictures of the preparation:

The 5 mean points

The 5 mean points

The inner parts

The inner parts

The inner piece of cake

The inner piece of cake

The whole marking

The whole marking

The inner square

The inner square

The complete labyrinth

The complete labyrinth

A total of 10 to 12 people were at work. Digging up the lawn could be done at the same time and at different places. The overrun lawn was taken away, on the way back the concrete paving stones (20 cm long, 10 cm wide) were brought, as well as the grit for the paving.
The laying of the paving stones began with the laying of the foundation stone in the middle of the central cross. Then from here were laid, beginning at the four ends of the cross, the 8 arcs of the labyrinth up to the respective inflection point (which at the same time are also centres). Through that no interpieces or passport pieces were necessary. Also this could already happen during the time of digging.

Here pictures of the construction:

Picture 1

Picture 1

Picture 2

Picture 2

Picture 3

Picture 3

Picture 4

Picture 4

Picture 5

Picture 5

Picture 6

Picture 6

Picture 7

Picture 7

Picture 8

Picture 8

Picture 9

Picture 9

Picture 10

Picture 10

Picture 11

Picture 11

Picture 12

Picture 12

Everybody has searched his work on its own, the teamwork arose by itself. A praise and a thank-you to all participants.
The labyrinth was ready with the laying of the “keystone” after 5 hours construction time.

Here the result:

Foundation stone

At work

At work

At work

Cap stone

Cap stone

The centre

The centre

The completed labyrinth

The completed labyrinth

View back

View back

Related posts

Read Full Post »

Older Posts »

%d bloggers like this: