With Arnol’d’s figures we already know all 8 alternating labyrinths with one arm and five circuits. Alternating means that the path does not traverse the axis. Whenever the pathway changes to another circuit it also changes direction from clockwise to anticlockwise (or vice-versa). Among these 8 labyrinths with 5 circuits there are 4 uninteresting, 2 interesting and 2 very interesting examples.
With an increasing number of circuits the number of different labyrinths increases rapidly. So there are 42 labyrinths with 7 circuits: 20 uninteresting, 16 interesting and 6 very interesting examples. The seed patterns for the walls and the patterns of the interesting and very interesting labyrinths are accessible on Tony Phillips’ website. These patterns generate six beautiful very interesting labyrinths. I therefore have reproduced the patterns and added the labyrinths in script form (i.e. on circular layout, with the entrance at the base of the design and in clockwise rotation). Here are the results:
Fig. 1: This is the well-known, most widespread labyrinth – the Cretan.
Fig. 2: A principle that appears also among Arnol’d’s figures: serpentine from the inside out. This can also be conceived as serpentine enclosed in a single double-spiral like meander (Erwin’s type 4 meander).
Fig. 3: A beautiful pattern with an S-shaped course of the pathway.
Fig. 4: Also a beautiful pattern – sort of a Yin/Yang movement.
Fig. 5: A serpentine enclosed by a two-fold double-spiral like meander (Erwin’s type 6 meander).
Fig. 6: This principle is also well known from Arnol’d’s figures: double-spiral type meander here in its three-fold manifestation (Erwin’s type 8 meander).
The Cretan type labyrinth therefore belongs to a group of six matching self-dual interesting alternating one-arm labyrinths with 7 circuits.