I use a different method to generate the related labyrinths than Andreas. But I’ll get the same result. This is how we complement each other.
Essentially, I am using the level or path (= circuit) sequence to get the version of a particular labyrinth I want. Also, I am taking the path sequence to construct the labyrinth, not the seed pattern.
I usually number from the outside in (the left digits in blue), additionally here from the inside to the outside (the right digits in green).
The level sequence for the basic labyrinth is here: 0-1-2-5-4-3-6. “0” stands for outside, “6” stands for the center. We have a 5 circuit labyrinth in front of us. “1” to “5” are the numbers of the circuits (paths), hence the path sequence 1-2-5-4-3 (fig. 1).
To create the dual labyrinth, I just use the green numbers on the right side of the basic labyrinth. I determine the level sequence by going outwards from the center. I get 6-3-2-1-4-5-0. Now I draw a labyrinth using this row of digits, going from the outside to the center. But first I replace “6” with “0” and “0” with “6”, I swap inside and outside as it were. The new level sequence is then: 0-3-2-1-4-5-6 (fig. 2).
The left numbers now indicate the level sequence: 0-3-2-1-4-5-6. If I now read the green numbers on the right side, I of course get the basic labyrinth again.
Now I use another technique to get the transposed labyrinth. I take the path sequence of the dual labyrinth, here: 3-2-1-4-5 and complement all numbers to “6”.
The second line, completed by “0” for the outside and “6” for the center, gives the level sequence for the transposed labyrinth: 0-3-4-5-2-1-6 (fig. 3).
But there is still a different technique to get there: I can read the path sequence from the basic labyrinth backwards and again complete with “0” and “6”.
The second line, completed by “0” for the outside and “6” for the center, also gives the level sequence for the transposed labyrinth: 0-3-4-5-2-1-6 (fig.3).
If I now take the green numbers of the right side, I’ll get the dual of this transposed labyrinth, which is the next, the complementary labyrinth with the level sequence: 0-5-4-1-2-3-6 (fig. 4).
But again there is also the above described technique to get the complementary labyrinth. I take the basic labyrinth and complement the numbers of its path sequence to “6”.
The second line, completed by “0” for the outside and “6” for the center, gives the level sequence for the complementary labyrinth: 0-5-4-1-2-3-6 (fig. 4).
I can also take the dual labyrinth and read the path sequence backwards, and again add “0” and “6”.
The second line, added with outside and center gives the level sequence for the complementary labyrinth: 0-5-4-1-2-3-6 (fig. 4).
If I now take the green numbers on the right side, I’ll get the dual labyrinth to this complementary labyrinth, namely the transposed labyrinth with the level sequence: 0-3-4-5-2-1-6 (fig. 3).
So we have seen three different ways to transform one labyrinth into another by using the path or level sequence.
However, it only takes two methods to create the appropriate labyrinths. I personally prefer the “transposing” technique and the “complementing” technique.
First we have the basic labyrinth (fig.1). Through transposing the path sequence of the basic labyrinth 1-2-5-4-3 into 3-4-5-2-1 I’ll then get the transposed labyrinth (fig.3).
This transposed labyrinth with the path sequence 3-4-5-2-1 I transform to the dual labyrinth by complementing the path sequence to 3-2-1-4-5 (fig.2).
This dual labyrinth I then transform to the complementary labyrinth by transposing its path sequence 3-2-1-4-5 into 5-4-1-2-3 for the complementary labyrinth (fig.4).
For control purposes, I can transform the basic labyrinth into the complementary by complementing the path sequence 1-2-5-4-3 of the basic into 5-4-1-2-3 (fig. 4) for the complementary.
All of these transformation methods have the same effect as the rotating and mirroring techniques by Andreas.