For every labyrinth exists a second or dual one. And in special cases the dual one looks like the original one. Then this is a self-dual labyrinth.
These connections should be explained here.
Andreas Frei has done this on his website under the topic “Grundlagen” (basics), to this day only in German. I expressly recommend to take a look at it, there are some meaningful drawings also.
Here again we will see it from the practical side. Hence, it is a continuation of the post from the 1st of September, 2013 about the circular 7 circuit labyrinths. Through the dual labyrinths here we will get six more to add to the seven there. So we will have 13 new labyrinths in all.
How we will reach for that, should be shown step by step. Maybe a little bit awkwardly, but I hope, understandably.
We number all labyrinths from the outside inwards in black. “0” stands for the outside and “8” for the center. The path sequence, that is the order in which we walk through the circuits to arrive at the center, is noticed on the bottom left in black.
Then we number all circuits once again from the inside outwardly in green. “0” is now the center and “8” is now the outside. We write down the circuits in the order in which we walk them while going backwards from the middle. This path sequence is noticed on the bottom right in green.
As already mentioned, there is to every (original) labyrinth a second (dual) one. And this arises when we interchange inside and outside, when we turn inside out. The path sequence which we will get, is normally different from the one of the original labyrinth.
If it is the same, we speak of a self-dual labyrinth. Then an internal symmetry is given. Or differently expressed: The rhythm and the motion sequence is the same when stepping inside or outside. In our examples this applies to the first (well-known Cretan) labyrinth, and to the last, a new labyrinth.
The remaining six have another path sequence and, hence, are to be taken for new, different labyrinths.
Here the six new types (click to enlarge, print or save):
These examples shows that always at first the middle is circled around. After that one moves inside the the labyrinth and finally one enters the center from the 3rd or the 5th circuit.
In the case of the types introduced in the last article the entry into the center was always from the outermost, the first circuit. Here we have the circling around the middle immediately after stepping into the labyrinth.
The motion sequences are completely different.
It would be of interest exploring that by a temporary or even a permanent labyrinth. Worldwide there are still no labyrinths of this kind.
The shape must not necessarily be perfectly circular. It is important only to adhere to the path sequence.
For the rest, they can be as simply build in sand like the types introduced in the below mentioned post.
- How to Make a Circular 7 Circuit Labyrinth and Seven New (up to now unknown) Circular 7 Circuit Labyrinths in Sand