World Labyrinth Day 2020: Drawing a Labyrinth

Once again (for the 12th time) the Labyrinth Society invites us to celebrate World Labyrinth Day.
As every year, it is the first Saturday in May, this year May 2nd, 2020.

Flyer of the Labyrinth Society

Flyer of the Labyrinth Society

The global corona pandemic is also affecting this day. Larger group events are usually not possible.
That is why the day should be celebrated differently than usual. There are many ways to do this.

The Labyrinth Society offers a 24-hour online event entitled Walk around the World, which virtually connects people on the GoToMeeting platform across time zones.
This requires registration. More information is available on the Labyrinth Society website:

Lars Howlett offers to use a finger labyrinth virtually and online.

Design © Lars Howlett

Design © Lars Howlett

This will take place in a zoom meeting on May 2nd, 2020 from 12:45 to 14:00 PM Pacific Time (USA and Canada), at which you can register here:

Here is a converter for the different time zones:

My proposal: Drawing a labyrinth

There are also many options and methods for this. Some have already been featured in this blog.
How about a labyrinth on empty toilet paper rolls? After all the hamster purchases, should there be enough?
Ariadne’s thread, the path in the labyrinth, is drawn directly. So we do not need a pattern, as we do it usually to draw the classic labyrinth.

Toilet paper rolls labyrinths

Toilet paper rolls labyrinths

How to do this is explained here.

Or do we draw the (boundary) lines for a Wunderkreis? The path runs between the lines here. It is a walk-through labyrinth with a choice.

The lines for a Wunderkreis

The lines for a Wunderkreis

The details are explained below:

But we can also draw the path in the labyrinth, Ariadne’s  thread:

Ariadne's thread in a Wunderkreis

Ariadne’s thread in a Wunderkreis (Kaufbeuren)

We see the method here:

For many, however, it will also be possible, as usual, to walk a labyrinth.

No matter how, World Labyrinth Day can be celebrated.
The Labyrinth Society is again organizing a survey.

If you are looking for a labyrinth near you, maybe you will find one here:

Related Posts

The Labyrinths with 3 Double-barriers, 4 Arms, and 5 Circuits

Sigmund Gossembrot has used the double-barrier as a new element for the design of labyrinths. His five-arm labyrinth on fol. 51 r (see: related posts 5) and the four-arm labyrinth hidden in the design on fol. 53 v (related posts 4) are made up exclusively of double-barriers in all side-arms. They have 7 circuits and are no sector labyrinths.

In a series of posts, Erwin has introduced new sector labyrinths with four arms, five circuits and double-barriers (related posts 1, 2, 3). He has based these designs on the 8 possible courses the pathway can take in a one-arm labyrinth with five circuits. Sector labyrinths can be obtained by stringing together such courses of the pathway. Theoretically there exist 4096 variations for an arbitrary stringing together of four out of 8 courses of the pathway. Erwin has shown some of them. However, not all did consistently employ the principle of the double-barriers.

Here I will address the question how many sector labyrinths there are with four arms, five circuits and consistently employing double-barriers. I also start with the 8 possible courses of the pathway. These are based on Arnol’ds’ meanders in fig. 1 (related posts 6).

Figure 1. The Meanders by Arnol’d

In fig. 2 I show the patterns that correspond with the meanders. The patterns bear the same numbers as the meanders they were derived from. The left side of the figure shows the patterns of all alternating one-arm labyrinths with five circuits. Each of hese patterns also contains a connection from the outside into the labyrinth (from top left) and a connection to the center (to bottom right). These connections are represented in grey. In order to be used as segments (sectors) in sector labyrinths, these patterns at first have to be considered without the grey connection lines. The question here is the course of the path inside the sector. In a sector labyrinth, multiple such patterns are stringed together. Only the first pattern contains a connection to the outside and only the last a connection to the center. The patterns representing the 8 possible courses in a sector are displayed in the box on the right side.

Figure 2. The Corresponding Patterns – Left Half: Patterns of the One-arm Labyrinths; Right Half: Patterns of the Sectors

Next we intend to string together such patterns of sectors and to generate four-arm labyrinths using exclusively double-barriers. Let us first have a look at such a double-barrier in the labyrinth type Gossembrot 51 r. Figure 3 shows the labyrinth with the Ariadne’s Thread drawn in (red). Except for the one-arm labyrinths, an axis always lies between two segments, is formed by two different segments. Let us choose the double-barrier at the third side-arm. This connects segments III and IV and lies on the outermost four circuits. In the scaled-up section the seed pattern for the walls delimiting the path is drawn-in in blue color. It can be seen, that two nested turns of the Ariadne’s Thread are mirrored symmetrically against the central piece of the wall delimiting the pathway. Four circuits are needed for the double-barrier. In a labyrinth with five circuits, only one circuit remains free for the passage from one sector to the next. From this it becomes clear, that labyrinths with five circuits and using exclusively double-barriers must be sector labyrinths. There is only one circuit for the path to traverse the arms. This implies that the pathway must have completed the previous sector entirely before changing to the next.

Figure 3. The Double-barrier as by Gossembrot

Figure 4 shows the admissible connections between the sectors. (Pro memoria: the lines represent the pattern, i.e. the Ariadne’s Thread in rectangular form). The double-barriers occupy four circuits side by side. So they can lie in two places on circuits 2 – 5 or on circuits 1 – 4. Only connections on the same circuits are allowed, that is, the two options on the outermost (a) or on the innermost (b) circuit. If we would consider to change to another circuit when connecting the segments, as shown in options c or d, this would result in the insertion of an additional axial piece of the path between the halves of the double-barrier and these halves would be shifted by one circuit one against the other. But this is not a double-barrier any more.

Figure 4. Admissible Connections between Sectors

This circumstance strongly limits the range of the possibilities for stringing together the patterns. Figure 5 shows, how the different patterns can be used. The red numbers, characters at the free ends of each pattern indicate with which patterns it can be connected there (number of pattern, E for entrance, Z for center). A four-arm labyrinth has four segments. These are therefore also referred to as „quadrants“.

Figure 5. Possibilities for the Use of the Patterns

  • Two patterns, no. 1 and no. 6 cannot be used at all. With these it is not possible to generate a double-barrier.
  • Four „one-sided“ patterns, that is no. 2, no. 4, no. 5, and no. 7 have only on one side a half of a double-barrier (circled in red). On this side they can be connected with other patterns to double-barriers. It is true that it is also still possible to connect pattern no. 2 with no 5, and pattern no. 4 with no. 7 (not indicated). However, such a connection results in a two-arm labyirinth with one double-barrier only. On the second side of these one-sided patterns the free end lies on the third circuit. There, no double-barrier can be generated. Therefore, on this side only a connection to the entrance or the center is possible. Thus, these one-sided patterns can only be placed next to the main axis. Pattern no. 2 and no. 7 can only be placed in quadrant IV, where they are connected with the center. Pattern no. 2. can further only be connected with no. 8, and pattern no. 7 can be connected with no. 3.
  • Only two patterns, no. 3 and no. 8 can be completed to double-barriers at both sides. And only these can be placed in quadrants II or III. Furthermore, they may also be placed in quadrants I or IV, and thus be connected with the entrance or with the center (not indicated). Patterns no. 3 and no. 8 can be stringed together alternately or they can be connected with other one-sided patterns (pattern no. 3 with no. 5 and no. 7; pattern no. 8 with no. 4 and no. 2).

This provides us with the basis for the generation of the patterns for the sector labyrinths with the double-barriers. We start with the patterns for the quadrants II and III. For these, there are only two arrangements. Pattern no. 8 can be attached to no. 3 (above) or pattern no. 3 can be attached to no. 8 (below). The upper combination can be supplemented with patterns no. 5 or no. 8 towards quadrant I, and with patterns no. 2 or no. 3 towards quadrant IV. The lower combination can be supplemented with patterns no. 3 or no. 4 towards quadrant I, and with patterns no. 7 or no. 8 towards quadrant IV.

With the upper combination of the patterns no. 3 and no. 8 in quadrants II and III, thus, four patterns of labyrinths with four arms, five circuits and a consistent use of double-barriers can be generated. These patterns are shown in fig. 6.

Figure 6. The Patterns with the Combination no. 3 in Quadrant II – no. 8 in Quadrant III

Also with the lower combination of the patterns no. 8 and no. 3 in quadrants II and III, four patterns of labyrinths with four arms, five circuits and a consistent use of double-barriers can be generated. These patterns are shown in fig. 7.

Figure 7. The Patterns with the Combination no. 8 in Quadrant II – no. 3 in Quadrant III

Figure 8 now shows the labyrinths corresponding to the patterns of fig. 6.

Figure 8. The Labyrinths Corresponding with the Patterns of Fig. 6

Finally, figure 9 shows the labyrinths corresponding to the patterns of fig. 7.

Figure 9. The Labyrinths Corresponding with the Patterns of Fig. 7

The question concerning the number of possible labyrinths can be clearly answered:

  • There exist 8 labyrinths with 3 double-barriers, 4 arms and 5 circuits.

Moreover, in addition to this question, we obtain the following findings:

  • Labyrinths with 5 circuits and fully employing double-barriers must be sector labyrinths.
  • Such labyrinths cannot have double-barriers at the main axis. Double-barriers are only possible at the side-arms.

Related Posts:

  1. New 5 Circuit Labyrinths with Double Barriers
  2. A new Generation of Sector Labyrinths
  3. A new type of Sector Labyrinth inspired by Gossembrot
  4. Sigmund Gossembrot / 3
  5. Sigmund Gossembrot / 2
  6. Considering Meanders and Labyrinths

A new type of Sector Labyrinth inspired by Gossembrot

I was particularly fascinated by the technique of double barriers in Gossembrot’s 7 circuit labyrinths presented in recent posts. This makes possible completely new types of labyrinths. He probably did not “invent” the double barriers, but he was the first to consistently and systematically use them.

How does this technique affect 5 circuit labyrinths?
I tried that and came across a whole new kind of sector labyrinths.
As you know, one sector after another is traversed in these before the center is reached.

The historical Roman labyrinths are divided into three different variants: the meander type, the spiral type and the serpentine type (see the Related Posts below).
The entry into the labyrinth is usually up to the innermost lane. And in all four sectors the structures are the same.
The change to the next sector either always takes place outside or even once inside (or alternately).

Now the new type:

The new sector labyrinth in concentric style

The new sector labyrinth in concentric style

What is so special about that?
Already the entrance: It takes place on the 3rd lane. This does not occur in any historical sector labyrinth. And the entrance into the center is also from the 3rd lane.

Then the structure expressed by the path sequence is different in each quadrant.

Quadrant I:   3-2-1-4-5
Quadrant II:  5-2-3-4-1
Quadrant III: 1-4-3-2-5
Quadrant IV: 5-4-1-2-3

The transitions to the next sector are always alternately.

Nevertheless, the new labyrinth is very balanced and mirror-symmetrical.

Here in a square shape:

The new sector labyrinth in square shape

The new sector labyrinth in square shape

This makes it easier to compare with the previously known Roman labyrinths (see below), which are mostly square.

The difference to these becomes clear especially in the presentation as a diagram. Because this shows the inner structure, the pattern.

The diagram for the new sector labyrinth

The diagram for the new sector labyrinth

Very nice to see are the nested meanders.

But even in Knidos style, this type is doing well:

The new sector labyrinth in Knidos style

The new sector labyrinth in Knidos style

How should one call this type? And who builds one as a walkable labyrinth?

Related Posts

A Golden Greek 50 Euro Commemorative Coin from 2017

In 2017, a commemorative coin dedicated to the Minoan civilization was issued by the Mint of the Central Bank of Greece.
This earliest civilization in Europe can be traced back to the years around 2600 BC. The Minoan civilization got its name from the famous King Minos. The story goes that, with the help of the god of the seas, Poseidon, and a white bull, he came to power and thus gained fame and reverence among his people.

The 50-euro gold coin from 2017 was issued with an edition of 1500 pieces and minted in real gold (999.9 / 1000) in the highest collector quality “polished plate”.

Here is the value side:

Value side: Hellenic Democracy 50 Euro

Value side: Hellenic Democracy 50 Euro

And here the picture side:

Picture side: Minoan Civilization 2017

Picture side: Minoan Civilization 2017

Two nested cross meanders can be seen in a large square around 5 smaller squares.
Here is the structure in a black and white tracing:

Draw up of the picture side

Draw up of the picture side

The black lines form two closed line systems without beginning and end. The white lines have branches and dead-ends, also without access. This is reminiscent of a similar representation on the silver coins of Knossos, which are well over 2000 years older (see related posts below).

Should the representation again symbolize the labyrinth of the Minotaur?

Related Posts