The Rings of the Auxiliary Figure
In the two previous posts I have presented the „Cretan“ and the Snail-Shell labyrinth in the Man-in-the-Maze (MiM-) style (see related posts below). Both have the same seed pattern and the same auxiliary figure. If we now try to draw other labyrinths with 7 circuits in the MiM-style, we’ll soon notice, that not all can be matched with the auxiliary figure with 11 rings. Although all have 16 spokes, some of them need less, others more than 11 rings. What’s the reason for that? I will show this with the two extreme examples.
The first labyrinth is comparable with the historical Löwenstein 3 (3 circuits), Näpfchenstein (5 circuits), or Casale Monferrato (6 circuits) labyrinths. I don’t know any historical example of such a labyrinth with 7 circuits. It is one of the 20 uninteresting labyrinths (see related posts below) with 7 circuits, although self-dual. The pattern of this labyrinth is made of a serpentine from the outside in. The seed pattern consists of 8 similar eigth parts. In the auxiliary figure this is the smallest possible seed pattern. This takes one circuit .
A labyrinth of this type, drawn in the MiM-style, requires an auxiliary figure with only 10 rings.
The second labyrinth is comparable with the historical Knossos (3 circuits), and (the core-labyrinth of ) Rockcliffe Marsh (5 circuits) labyrinths. I am not aware of a historical example of such a labyrinth with 7 circuits either. It is one of the six very interesting labyrinths (see related posts) with 7 circuits. The pattern is made-up of a double-spiral like meander. Whereas the Knossos-type labyrinth consists of a single (Erwin’s type 4) meander and Rockcliffe of a two-fold (type 6) meander, this labyrinth is based on the three-fold (type 8) meander. The seed pattern consists of two identical halves. Each is composed of four nested turns. This is the largest possible seed pattern for a labyrinth with 7 circuits in the auxiliary figure. For this, four circuits are needed.
A labyrinth of this type, drawn in the MiM-style, requires an auxiliary figure with 13 rings.
Both seed patterns have 16 ends and the auxiliary figures have the same number of spokes. This is the same for all labyrinths with 7 circuits (colored in blue in the figure below).
The number of rings needed for the auxiliary figure depends on three factors:
- the number of circuits of the labyrinth
- plus one additional circuit for the center
- the number of circuits needed for the seed pattern
The number of circuits for the seed pattern depends on how deeply nested it is. In a labyrinth with 7 circuits, this can vary from a series of single, not nested, turns up to four nested turns. These two extremes are colored in red in the above figures. The lower extreme requires 1, the upper 4 circuits.