There are eight possibilities for a one arm 5 circuit labyrinth (see Related Posts below).
The structure of the different labyrinths can be expressed through the path sequence. Here is a list:
The sector labyrinth presented in my last post (see Related Posts below) has a different path sequence in all 4 quadrants. In other words, there are 4 different labyrinths hidden in it. These were the path sequences in the 1st to the 4th line of the list above.
Today another 5 circuit sector labyrinth modeled with Gossembrot’s double barrier technique:
The path sequence in quadrant I is: 3-4-5-2-1, in quadrant IV: 1-2-5-4-3. These are the aforementioned courses at the 5th and 6th place. The two upper quadrants have: 1-4-3-2-5 and 5-2-3-4-1. These correspond to the upper pathways at the 4th and 3rd places. Not surprising, because the transition in these sector labyrinths takes place either on the 1st or the 5th course.
Here in a representation that we know from the Roman labyrinths:
Or here in Knidos style:
On Wikimedia Commons I found this picture of Mark Wallinger’s unique Labyrinth installation at Northwood Hills station, installed as part of a network-wide art project marking 150 years of the London Underground. It is part of the emboss family (one of the 11 labyrinth design families).This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
Now only two path sequences are missing, then we would have the eight complete.
There is also a new sector labyrinth for this:
In the two lower quadrants we have the courses 1-2-3-4-5 and 5-4-3-2-1. These are the above mentioned pathway sequences at the the 7th and 8th places. The upper two sequences (5-2-3-4-1 and 1-4-3-2-5) are again identical to the aforementioned two labyrinths and the one in the previous post.
The quadratic representation shows that it is actually a mixture of serpentine type and meander type (see Related Posts below).
Here in Knidos style:
Simply put, in only three sector labyrinths can all theoretically possible eight 5 circuit labyrinths be proved.
But it is also possible to move the “upper” pathways down, so that again arise new display options.
Then you can swap the right and left “lower” quadrants.
Or mirror everything and create right-handed labyrinths.
Here are two examples: