Today we will see the Snail Shell labyrinth in square form.
We build the labyrinth by strictly using the given path sequence, but we don’t cross the central axis. Thus the path several times changes the direction. This again produces the pendular movement how it is demanded for a “right” labyrinth. There arise four turning points.
A more exact view also shows the hidden type Knossos inside, and that only at the beginning and at the end two circuits with change of course were added. Andreas has already pointed to that.
The following drawing shows the walls in black, the seed pattern is highlighted in colour.
Nevertheless, another new type of labyrinth turned up indirectly via the derivation of the Snail Shell labyrinth from the seed pattern by the construction after the path sequence. Though with the creative defects of the beginning on the first circuit and the entry into the middle from the last circuit. However, at least, it is self-dual.
The seed pattern for this type I developed belatedly. It looks quite different as the meanwhile well-known pattern for the Classical 7 Circuit Labyrinth.
Much different looks the labyrinth if one uses all the four crossings of the axis which are possible, even though keeping up the path sequence.
There remains only two turning points with changes of direction: When changing from the 5th to the 4th circuit, and when changing from the 4th to the 3rd. For the rest one advances forwards in a spiral-shaped movement, just as in a snail shell.
If one arranges the entrance edgeways, one can fill up the whole square. One could still procreate other shapes by twisting and mirroring the figure.