In one-arm labyrinths, each circuit is represented by one number. Therefore it is possible to capture even quite large labyrinths appropriately with the level sequence. In labyrinths with multiple arms, the pathway may repeatedly encounter the same circuit. Various possibilities exist to take account of this in the level sequence. For this, according to the number of arms, the circuits have to be further partitioned to segments. Here I will show a method in which all segments are numbered through.
For this I use an example of a labyrinth that has repeatedly been presented on this blog. It has 3 arms and 3 circuits.
First, each circuit is partitioned to three segments. One segment corresponds with a unit of the pathway between two arms. Next, the segments have to be numbered through. This can be done in different ways. Here I number them from the outside to the inside and one circuit after each other.
Now we can track the course of the pathway through the various segments. This results in the sequence of segments encountered by the pathway. In labyrinths with multiple arms the level sequence thus extends to a sequence of segments.
The sequence of segments of this labyrinth is 7 4 1 2 5 8 9 6 3. The length of this sequence of numbers is a result of the number of circuits multiplied with the number of arms. Thus, for a labyrinth with 3 circuits and 3 arms, 9 numbers are required. Whereas in a one-arm labyrinth with 3 circuits only 3 numbers are needed.
However, besides the numbers no other information is needed. The sequence of segments itself determines where the pathway makes a turn or traverses an axis. In one-arm labyrinths this had to be indicated additionally by use of separators.
Posted in Design, Labyrinth | Tagged labyrinths with multiple arms, level sequence, one-arm labyrinths, sequence of segments | 2 Comments »
Finally, I got around to visiting this unusual labyrinth from granite ashlars in the Fichtelgebirge.
You may reach it over the street from Kleinschloppen to Kirchenlamitz. There is a parking place opposite the restaurant Waldschmiede in the district Buchholz and directly behind it lies the labyrinth.
Willi Seiler from Wunsiedel, a former professional schoolteacher in the technical school for stone processing in Wunsiedel had the idea of the labyrinth. The construction works were carried out after the plans of architect Peter Kuchenreuther from Marktredwitz in 2009.
The labyrinth is from type Roman sector labyrinth with a meander in every quadrant and has 5 circuits. It is put on squarely and has the dimensions 34 x 34 m. The middle is a square of 6 m sides length with a 5-m-high obelisk, where Hermann Kern’s famous words: “In the labyrinth you will not get lost. In the labyrinth you will find yourself. In the labyrinth you will not meet the Minotaurus. In the labyrinth you will meet yourself.” are chiseled.
The ways and the granite bolders are each about 1.20 m wide. The higher ashlars in the middle and around are about 1.20 m high, the smaller ones inside from 60 to 80 cm. In every quadrant there is a small loophole to leave the way which amounts to 400 m after all. The middle contains the obelisk, some wooden benches and the ground is covered with a paved labyrinth showing the paths enlargedin black stones as it were a negative of the “big” labyrinth.
The middle enlarged:
Behind the labyrinth a small hill is raised from which one can overlook the whole area. Several boards of information to the geology, fauna, granite quarrying in the Fichtelgebirge among other things as well as to the idea of the labyrinth are put up on the site.
Service station for spirit and soul
Service station for spirit and soul
Labyrinths still are in the world since millenniums in the most different forms. After Ancient Greek myth the first labyrinth was built by Dädalos for king Minos on Crete as a prison for the Minotauros. In the antiquity it is often shown as a square built by windings of meanders. The Christians pervaded this ancient motive with new sense. In many old churches labyrinths drawn on the ground with black and white stones show with their unpredictable bends the human life with all its scrutinies, delays and complications, while in the middle, the aim, waits heavenly Jerusalem.
The labyrinth is always purposeful and not a maze, how frequently is falsely presumed.
„The construction plan of the labyrinth is conceivably simple. It has an entrance and a way which leads in numerous bends to a middle. One can go through it fast without having found out something. Then the way through the labyrinth is not more than just a leisure activity or a sportive act. Who crosses, however, the way with a spiritual feeling, who embarks on a journey consciously and with alert soul, will attain a place of self-encounter and self-discovery.“ Uwe Wolff
Posted in Labyrinth, Report, Typology | Tagged meander, roman labyrinth, sector labyrinth | Leave a Comment »
In an earlier post „Type or Style / 6“ (see related posts, below) I had already mentioned the level sequence. And I had stated two reasons for why I do not use it for naming types of labyrinths.
- Among the one-arm labyrinths only in alternating labyrinths there exists exactly one type of labyrinth for each level sequence. If we also consider non-alternating labyrinths, in which the pathway traverses the axis, there can exist multiple courses of the pathway for the same level sequence.
- In labyrinths with multiple arms the level sequence may rapidly increase to a length and complexity that is difficult to memorize.
Here I want to address the first issue further. I do this because there is a very simple solution for it. In one-arm labyrinths every circuit is represented by one number. In real practice only few of the larger labyrinths will have more than 15 – 17 circuits. Most one-arm labyrinths have a markedly smaller size. Therefore these labyrinths could be quite simply be named with their level sequence. But there remains the problem with the ambiguity. Erwin had elaborated on it in his post “The Classical 7 Circuit Labyrinth with Crossed Axis“ (see related posts, below). I will illustrate it here and use some figures of Erwin’s post.
Figure 1. Level Sequence 3 2 1 4 7 6 5
In Figure 1 three labyrinths with the level sequence 3 2 1 4 7 6 5 are shown. The first image shows the alternating Cretan type, the second and third images show non-alternating labyrinths with the same level sequence. In the second image, the pathway traverses the axis when changing from the 1st to the 4th circuit. In the third image it traverses the axis from the 4th to the 7th circuit. (There is an other labyrinth with the pathway traversing the axis twice, first from the 1st to the 4th and second from the 4th to the 7th circuit). We thus are here presented with the only one alternating and several non-alternating types of labyrinths with the same level sequence.
Now there is a simple solution, to take account of this in the level sequence. For this it has to be considered, that the single numbers (not numerals) of the level sequence are separated. This separation can be obtained in different ways, using blanks, commas, semicolons etc. These separators, however, can also be used to indicate how the path will continue on the next level. Therefore we could e.g. define: if the path changes direction from the former to the next circuit, we will separate the numbers with a vertical slash. If, on the other hand, the path continues in the same direction and thus traverses the axis, we separate with a hyphen. This enables us to specify the level sequence so that it is unique also in non-alternating labyrinths. I show this in figure 2 using the images from figure 1.
Figure 2. Level Sequence with Separators
Here we see for each labyrinth the unique level sequence with separators. The sequence of numbers is the same 3 2 1 4 7 6 5 in all three labyrinths. However, whereas in the alternating Cretan type all numbers are separated by slashes (as the path always changes direction when progressing from one circuit to an other), the level sequence in the second labyrinth is written with a hyphen between 1 and 4, and the level sequence in the third image with a hyphen between 4 and 7.
Indeed, the notation can be even simplified by separating with blanks and using hyphens only to indicate where the pathway traverses the axis. The level sequences would then be written as follows:
for the 1st image: 3 2 1 4 7 6 5
for the 2nd. image: 3 2 1-4 7 6 5
for the 3rd image: 3 2 1 4-7 6 5
What matters is that in the level sequence it is indicated where the path traverses the axis. With this specification it is now possible to give a unique level sequence to each course of the pathway and thus a unique name to each alternating and non-alternating type of labyrinth.
Posted in Labyrinth, Typology | Tagged alternating, course of the pathway, level sequence, non-alternating, one-arm | 2 Comments »
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 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.
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.
Arriving at the second turning point there is a special moment: They meet each other and their lanes cross.
Shifting the lane
But they don’t change direction. They continue their way.
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 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.
Posted in Report, Typology | Tagged Appleton, baltic wheel, dance, ritual | 2 Comments »
In the last post I have presented four variants of the seed pattern of the Cakra Vyuh type labyrinth. Perhaps somebody might be interested, how the matching complete labyrinths look like. Here I will show them.
I thus add three other examples to the only example (Original) of this type of labyrinth that has been well known until now. Or, more exactly, only two of them are really new: the examples in the Classical and in the Concentric styles. I had already published the example in the Man-in-the-Maze style previously on this blog. Furthermore it has to be considered, that the original labyrinth rotates anti-clockwise. I have horizontally mirrored the three other examples. It is still the same labyrinth then, although rotating clockwise. I use to show all my labyrinth examples in clockwise rotation so they are more easily comparable.
Posted in Design, Labyrinth | Tagged Cakra-vyuh, concentric, Klassical, man in the maze, style, type | Leave a Comment »
This is what a Baltic Wheel looks like:
The Baltic Wheel
It has circuits which run primarily about two turning points. The middle is empty, however, it has a second, short way to leave it directly. Thereby we also have two entries which are separated by a spoon-like formed part.
Historical examples are very rare. In Germany there is the Rad in der Eilenriede at the town park of Hannover. Otherwise we only know this type from literature.
In the previous articles I have dealt with the Wunderkreis. Besides, a certain resemblance between both these types has also struck me. Though both have two entries they are still different types. In what way are they different now?
The labyrinthine circuits are disposed around turning points which are arranged in a triangle. In the middle we have a double spiral (the circuits A, B, C) through which we leave the Wunderkreis. We have a walk-through labyrinth lying ahead of us.
The Baltic Wheel has a big, empty middle and consequently contains no double spiral. However, there is also the second access (or exit). If I leave out the circuits for the double spiral, I shall nearly get the Baltic Wheel.
The intermediate stage
The remaining circuits are the same. Also the path sequence is the same. This shows the close relationship between the two labyrinth types.
Now I add a middle section formed from arcs between the two entrances and will thus receive a complete Baltic Wheel.
The Baltic Wheel
The Baltic Wheel can exist of a varied number of circuits. These can be added the same way as in the Wunderkreis (see related posts below).
Other design elements can also be added, such as an additional circuit around the whole Baltic Wheel.
Some years ago I had already published construction instructions for the Baltic Wheel. It looked a little bit different. The construction developed now seems easier to me and I like it better.
If I have fixed the number of the circuits for a Baltic Wheel, I can also begin with the base line of the triangle (between M3 and M4) and then determine the centre M1.
The construction has a dimension between axes of 1 m and therefore allows to scale it easier.
Here as a PDF file to look at, to print or to copy.
Posted in Design, Labyrinth, Typology | Tagged baltic wheel, double-spiral, Wunderkreis | 1 Comment »
In the last post I have introduced the eleven-circuit Cakra Vyuh Labyrinth. Even though the seed pattern has a central cross and also can be easily drawn freehand, it is not a labyrinth in the Classical style. In fig. 1 I show the seed pattern in different variants.
Figure 1. Variants of the Seed Pattern
Image a shows the original seed pattern, image b the seed pattern in the Classical style, image c in the Concentric style, and image d in the Man-in-the-Maze style.
This figure clearly shows that the original seed pattern deviates from the Classical style. It is true that this seed pattern has a central cross as for instance the Cretan labyrinth also. However in the Cakra Vyuh seed pattern, from this cross further junctions branch off.
This is different in the Classical style. The Classical style consists of verticals, horizontals, ankles and dots. For this, no central cross is required. This page illustrates well, what I mean (left figure of each pair). If a seed pattern includes ankles these lie between the cross arms and do not branch off from them.
The four images in fig. 1 in part look quite different one from each other. So how do I come to the assertion that they are four variants of the same seed pattern? Let us remember that these figures show seed patterns for the walls delimiting the pathway. Now let us inscribe the seed patterns for the Ariadne’s Thread into these figures (fig. 2).
Figure 2. With the Seed Pattern for the Ariadne’s Thread Inscribed
At first glance this looks even more complex. However, if we focus on the red figures, we will soon see what they have in common.
Figure 3. Seed Pattern for the Ariadne’s Thread
The seed pattern represents a section of the entire labyrinth. More exactly, it is the section along the axis of the labyrinth. The turning points of the pathway align to the axis. This can be better seen on the seed pattern for the Ariadne’s Thread compared with the seed pattern for the walls delimiting the pathway.
In all four seed patterns, turns of the pathway with single arcs interchange with turns made-up of two nested arcs. This constitutes the manner and sequence of the turns and is the basic information contained in the seed pattern. In the four seed patterns shown, the alignment of the turns may vary from circular (image a, image d) to longisch, vertical, slim (image b, image c). The shape of the arcs is adapted to the shape of the walls delimiting the pathway. However in all images it is a single turn in alternation with two nested turns.
Posted in Design, Labyrinth | Tagged Ariadne's Thread, Classical style, Concentric style, Man-in-the-Maze style, seed pattern, walls delimiting the pathway | 1 Comment »