Up to now I have examined only sector labyrinths with four arms. The real double-barrier, however, originates from the five-arm labyrinth type Gossembrot 51r. As we know, this is not a sector labyrinth and it has 7 circuits. Now I want to find out, how many sector labyrinths with five arms and exclusively real double-barriers there are. Such labyrinths must have five cirucits. Therefore, we can use the same six sector patterns we have already used for the four-arm sector labyrinths.
In these four-arm labyrinths, only two sector patterns could be placed in every quadrant, i.e. sector patterns no. 3 and no. 8. Four sector patterns could only be placed in the quadrants next to the main axis (related posts 2). Now this is not different either in labyrinths with five arms. However, we then have to fill not only four quadrants, but the five sectors I til V with sector patterns. Sectors I and V lie next to the main axis. In the three sectors II, III, and IV between them, only sector patterns no. 3 or no. 8. can be placed. These can be arranged in only two different sequences, 3 8 3 or 8 3 8.
Figure 1 shows how the first sequence can be completed with patterns for sectors I and V. In sector I the two sector patterns no. 5 or no. 8 can be connected to the sequence 3 8 3. In sector V, sector patterns no. 7 or no. 8 can be attached.
Figure 1. Combinations with the Sequence 3 8 3 in the Sectors II – IV
In fig. 2 we can see, how the second sequence can be completed to a full five-arm labyrinth. Here, in sector I the sector patterns no. 3 or no. 4, in sector V the sector patterns no. 2 or no. 3 can be attached to the sequence 8 3 8 between them.
Figure 2. Combinations with the Sequence 8 3 8 in the Sectors II – IV
Figure 3 shows the four patterns and labyrinths that can be generated with the first sequence (3 8 3 from fig. 1).
Figure 3. Patterns and Labyrinths with the Sequence 3 8 3 in the Sectors II – IV
Figure 4 shows the four patterns and the corresponding labyrinths that can be generated with the second sequence (8 3 8 from fig. 2).
Figure 4. Patterns and Labyrinths with the Sequence 8 3 8 in the Sectors II – IV
Just as in the four-arm labyrinths, there exist also 8 different five-arm labyrinths made-up exclusively of real double-barriers. Even though they have only five circuits, they strongly remind us to the labyrinth type Gossembrot 51 r. We can also name them following the same rule as for the four-arm labyrinths (related posts 1). The name, thus, is composed of an uppercase letter followed by a number of marks. However, since these labyrinths have four side-arms, also four marks have to be attached to each uppercase letter. These marks indicate how the sectors are connected to each other. We have here exclusively real double-barriers with direct connections. Therefore, each name is composed of an uppercase letter followed by four horizontal marks.
- Classifying the Labyrinths with 3 Double-barriers, 4 Arms, and 5 Circuits
- The Labyrinths with 3 Double-barriers, 4 Arms, and 5 Circuits