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Posts Tagged ‘type Otfrid’

The Spokes of the Auxiliary Figure

In all earlier posts on this subject I have considered labyrinths with 7 circuits. The auxiliary figures of these labyrinths all have 16 spokes. The number of spokes of the auxiliary figure is determined by the number of the ends of the seed pattern. I will show this here for some selected labyrinths with less or more than 7 circuits. The first two examples are the only alternating labyrinths with three circuits. The third is a labyrinth with 11 circuits.

Type Löwenstein 3

Type Löwenstein 3

The simpler labyrinth with three circuits is of the Löwenstein 3-type. The seed pattern of this labyrinth has 8 ends. The pattern is made-up of a serpentine from the outside in. This labyrinth again contains the smallest possible seed pattern that covers only one circuit in the MiM auxiliary figure. Therefore the auxiliary figure has 8 spokes and consists of three circuits for the labyrinth, one for the center and one more for the seed pattern. For the boundaries of the five circuits, six rings are needed.

Type Knossos

Type Knossos

The other is the well-known Knossos-type labyrinth. The auxiliary figure for this type of labyinth has also 8 spokes. The pattern of this labyrinth, however, is made-up of a single double-spiral like meander (Erwin’s type 4 meander). This has two nested turns on each half of the seed pattern. It is this the largest possible seed pattern for a labyrinth with three circuits in the MiM-style. The seed pattern covers two circuits. Therefore, the auxiliary figure for this labyrinth needs 6 circuits / 7 rings, which is one more than the Löwenstein-type labyrinth.

As a third example I show the Otfrid-type labyrinth in the MiM-style.

Type Otfrid

Type Otfrid

Ths seed pattern of this type of labyrinth has 24 ends as is the case with all other labyrinths with 11 circuits. Thus, the auxiliary figure has 24 spokes. In addition the seed pattern consitsts of six similar sixth parts, each of which is made-up of two nested turns. It therefore covers two circuits. The auxiliary figure thus has 11 circuits for the labyrinth plus one for the center and two for the seed pattern, in all 14 circuits and 15 rings.

Seed Patterns with Single (Erwin's Type 4) Meanders

Seed Patterns with Single (Erwin’s Type 4) Meanders

The seed patterns of the Knossos-, Cretan- and Otfrid-type labyrinths all need two circuits in the MiM auxiliary figure. Remember that the Knossos type labyrinth is made-up of one, the Cretan of two and the Otfrid-type labyrinth of three single double-spiral-like (Erwin’s type 4) meanders. These are the three labyrinths of the horizontal line of the labyrinths directly related with the Cretan labyrinth.

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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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After the discovery of the “true” meander we will now come to the meander technique. What should this be?
In previous articles I have shown how one can generate a labyrinth from different meanders. The result were partly already known labyrinth types, but also up to now unknown types.

The mostly known 7 circuit  classical labyrinth is generated from the also well-known seed pattern. Most of the historical labyrinths with one axis have probably been constructed the same way. One could call this procedure the seed pattern method.

However, a 7 circuit classical labyrinth can also be generated from two joined meanders of the type 4. If I now make a row of more meanders, I can derive a line sequence from it and produce a labyrinth. I would like to call this the meander technique.

From 1 meander of the type 4 I will obtain a 3 circuit labyrinth with 2 turning points and the path sequence 0-3-2-1-4.

A 3 circuit meander labyrinth

A 3 circuit meander labyrinth

I can name the labyrinth: 3 circuit classical labyrinth with a larger center or 3 circuit Knidos labyrinth or 3 circuit meander labyrinth or Knossos labyrinth.
I could add: with 2 turning points and the path sequence 0-3-2-1-4.
In the catalogue of Andreas Frei this type is called “Knossos“.


From 2 meanders of the type 4 I will obtain a 7 circuit labyrinth with 4 turning points and the path sequence 0-3-2-1-4-7-6-5-8.

A 7 circuit Knidos labyrinth

A 7 circuit Knidos labyrinth

I can name the labyrinth: 7 circuit classical labyrinth with a larger center or 7 circuit Knidos labyrinth.
It is the oldest and most widespread labyrinth and also known as Cretan labyrinth.
I could add: with 4 turning points and the path sequence 0-3-2-1-4-7-6-5-8.
In the catalogue of Andreas Frei this type is called “Das Kretische“.


From 3 meanders of the type 4 I will obtain a 11 circuit labyrinth with 6 turning points and the path sequence 0-3-2-1-4-7-6-5-8-11-10-9-12.

A 11 circuit Knidos labyrinth

A 11 circuit Knidos labyrinth

I can name the labyrinth: 11 circuit classical labyrinth with a larger center or 11 circuit Knidos labyrinth.
The design for this labyrinth is known from a script from 868 AC and generally called type Otfrid.
I could add: with 6 turning points and the path sequence 0-3-2-1-4-7-6-5-8-11-10-9-12.
In the catalogue of Andreas Frei this type is called “Otfrid“.


From 4 meanders of the type 4 I will obtain a 15 circuit labyrinth with 8 turning points and the path sequence 0-3-2-1-4-7-6-5-8-11-10-9-12-15-14-13-16.

A 15 circuit Knidos labyrinth

A 15 circuit Knidos labyrinth

I can name the labyrinth: 15 circuit classical labyrinth with a larger center or 15 circuit Knidos labyrinth.
I could add: with 4 turning points and the path sequence 0-3-2-1-4-7-6-5-8-11-10-9-12-15-14-13-16.
This labyrinth is historically unknown as far as I know, thus a new type.


The series could be continued and I would get nothing but new labyrinths.
The principle might be clear: I attach a meander more and will get four more circuits (if I have type 4).

The rules: Each meander has 2 turning points. The number of the circuits results in the formula: C = (a x b) – 1. C stand for the number of circuits, a for the number of meanders, and b is the number of the type.

We apply this now to type 6 and look at the labyrinths generated from it.

From 1 meander of the type 6 I will obtain a 5 circuit labyrinth with 2 turning points and the path sequence 0-5-2-3-4-1-6.

A 5 circuit meander labyrinth

A 5 circuit meander labyrinth

I can name the labyrinth: 5 circuit classical labyrinth with a larger center or 5 circuit Knidos labyrinth.
I could add: with 2 turning points and the path sequence 0-5-2-3-4-1-6.
This labyrinth is historically unknown as far as I know, thus a new type.


From 2 meanders of the type 6 I will obtain a 11 circuit labyrinth with 4 turning points and the path sequence 0-5-2-3-4-1-6-11-8-9-10-7-12.

A 11 circuit Knidos labyrinth

A 11 circuit Knidos labyrinth

I can name the labyrinth: 11 circuit classical labyrinth with a larger center or 11 circuit Knidos labyrinth.
It corresponds to the 11 circuit classical labyrinth that can be generated from the enlarged seed pattern and forms the basis of most historical Troy Towns. However, there it has a smaller middle.
I could add: with 4 turning points and the path sequence 0-5-2-3-4-1-6-11-8-9-10-7-12.

In the catalogue of Andreas Frei this type is called “Hesselager“.


From 3 meanders of the type 6 I will obtain a 17 circuit labyrinth with 6 turning points and the path sequence 0-5-2-3-4-1-6-11-8-9-10-7-12-17-14-15-16-13-18.

A 17 circuit Knidos labyrinth

A 17 circuit Knidos labyrinth

I can name the labyrinth: 17 circuit classical labyrinth with a larger center or 17 circuit Knidos labyrinth.
I could add: with 6 turning points and the path sequence 0-5-2-3-4-1-6-11-8-9-10-7-12-17-14-15-16-13-18.
This labyrinth is historically unknown as far as I know, thus a new type.

Also here I could continue. However, that would generate only gigantic and “unwieldy” labyrinths.

We rather go to type 8.

From 1 meander of the type 8 I will obtain a 7 circuit labyrinth with 2 turning points and the path sequence 0-7-2-5-4-3-6-1-8.

A 7 circuit meander labyrinth

A 7 circuit meander labyrinth

I can call the labyrinth: 7 circuit classical labyrinth with a larger center or a 7 circuit Knidos labyrinth.
I could add: with 2 turning points and the path sequence 0-7-2-5-4-3-6-1-8.
This labyrinth is historically unknown as far as I know, thus a new type.


From 2 meanders of the type 8 I will obtain a 15 circuit labyrinth with 4 turning points and the path sequence 0-7-2-5-4-3-6-1-8-15-10-13-12-11-14-9-16.

A 15 circuit Knidos labyrinth

A 15 circuit Knidos labyrinth

I can name the labyrinth: 15 circuit classical labyrinth with a larger center or 15 circuit Knidos labyrinth.
It corresponds to the 15 circuit classical labyrinth that can be generated from the enlarged seed pattern and forms the basis of some historical Troy Towns. However, there it has a smaller middle.
I could add: with 4 turning points and the path sequence 0-7-2-5-4-3-6-1-8-15-10-13-12-11-14-9-16.
In the catalogue of Andreas Frei this type is called “Tibble“.

From 3 meanders of the type 8 we will obtain 23 circuits in accord with the formula: (3 multiplied by 8) minus 1 = 23 circuits with 6 turning points. This we save.

We will get with this method which I would like to call meander technique, known as well as up to now unknown labyrinth types.

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