2. Troja labyrinths

 

Using a basic figure of a cross + 4 corner dots and maybe some corner angles to draw lines or arches we get the walls for an interesting system of labyrinths known for 3000  years in much of the world. These labyrinths will here be called troja 1, troja 2 etc. and it will be shown how they can be varied and fitted to different demands.

 

 

Symbols and units:

See the section on labyrinths in roma style.

 

 

Contents for figures:

 

Fig. tr1: Troja 1, round, square, and rectangular

Fig. tr2: Troja 2, with lane pattern

Fig. tr3: Troja 3, with lane succession

Fig. tr4: Troja 2, complete square, multiple choice lanes

Fig. tr5: Troja 1, with a centre spiral

Fig. tr6: Troja 1, triangular

Fig. tr7: Troja 2, wave analysis

Fig. tr8: Troja 1, 2, 3 straightened out

 


 

Tegninger af troja 1 ud fra et kors + 4 prikker

Fig. tr1: Troja 1, round, square, and rectangular

Troja 1 labyrinth. (Often called 3 circuit). The most simple troja labyrinth, or trojaborg labyrinth named after Trojaborg on the island of Gotland in Sweden.

The “walls” between the lanes (or the dividing lines or the space between lanes) are constructed as shown in detail A using a basic figure of a cross and 4 corner-dots.

The labyrinth can be drawn in rounded form as shown in A or in square form as shown in  B, C, and D, with the complete square form in C.

In detail E only the walking lane is shown (for other types of labyrinths often only the lane is shown).

Troja 1 can be stretched to rectangular form as shown in detail F and G.

A spiral form is shown in fig. tr5 and a triangular form is shown in fig. tr6 below.

Troja 1 complies with wave figur B as described in fig. r1 in section 4 about labyrinths in roma style.

As best seen in detail A the troja labyrinths have a characteristic lopsidedness at the entrance side from right to left, which can be felt a disadvantage in planning a regular square or garden area to use this labyrinth. To conceal this lopsidedness detail C shows a small wall to the left of the entrance, which either moves the entrance to the corner or let the labyrinth start by having a small blind lane to the left of the entrance, as shown in fig. e1 and fig. e2. See also fig. tr8 below and fig. e5 with troja labyrinths straightened out by stretching.

Specialists on labyrinths and lovers of cultural history and historic labyrinths find the lopsidedness of the troja labyrinths an interesting distinctive feature that emphasizes this labyrinth and its ancient cultic mystery.

 

 

 

Tegninger af troja 2 ud fra et kors + 4 vinkler + 4 prikker

 

 

Fig. tr2: Troja 2, with lane pattern

Troja 2 labyrinth. (Often called 7 circuit). The most used troja labyrinth. It is found in different cultures in most of the world, e.g. the Mediterranean, in Scandinavia, in North America, in India. The oldest description of sure known origin found so far is on the back of a clay tablet from Pylos in Greece year -1200. Troja 2 is in round or square form found as Trojaborg labyrinth from Gotland, frescos in Nordic churches and around in Scandinavia for medieval dance, and drawn in Pompeii to show where the monster lives.

The labyrinth walls are designed using a cross + 4 angles + 4 corner dots.

The lane pattern with its interesting succession is shown in detail B and detail E.

Troja 2 is shown below as a regular square in fig. tr4 and fig. tr8. See also troja 2 in fig. e2, fig. e3, fig. e4, and fig. e5. 

Troja 2 complies with wave figur C, as shown in detail below in fig.tr7.

Tegning af troja 3 ud fra et kors + 8 vinkler + 4 prikker

Fig. tr3: Troja 3, with lane succession

Toja 3 labyrinth. (Often called 11 circuit). A big labyrinth which is seen at some places, e.g. the fresco in Hesselager Church in fig. i2.

The basic figure for constructing the walls is a cross + 4 big angles + 4 small angles + 4 corner dots, as shown in detail A.

As indicated the labyrinth can be drawn in other figures than round and rectangular.

The labyrinth can be stretched to a complete square or other rectangular forms as shown for troja 1 and troja 2.

By inserting more angles bigger labyrinths can be drawn (troja 4 etc.)

Troja 3 complies with wave figur D.

Tegning af troja 2 kvadratformet, og af troja 2 med blindgange

Fig. tr4: Troja 2, complete square, multiple choice lanes

Troja 2 made to a complete square and troja 2 with blind lanes and multiple choice lanes.

(Blind lane = dead end lane; multiple choice lanes = forked lane, many paths, multicursal).

On the drawing of troja 2 a horizontal line is placed just below the centre and all vertical lanes are stretched 1 (=1 lane width) to get a complete square as shown in detail A.

By inserting 1 or 2 extra lanes as shown in detail B we get a labyrinth with blind lanes if we close the end walls and we get a labyrinth with multiple choice lanes if the end walls are open. (Transverse walls and openings should not be placed just anywhere. The troja style should be kept with the long similar lanes. The style on the drawing with a stem and a crown with big firmament should be kept).

Example: The ?1-wall is closed and the ?2-wall is opened. If you walk furthest towards the centre from the start to walk lane B2 and coming to the other side of the stem choose the first lane to the left you end again at the start. If you next time from start choose the next lane = lane B1 you end in a blind lane. If you by start choose lane 1 and on the right side of the stem turn to the right (because it is closer to the centre) you end by start. This solution is used as square 20 troja labyrinth in fig. e3 in section 7 on this website.

Tegning af troja 1 udvidet med en spiral i midten

Fig. tr5: Troja 1, with a centre spiral

Troja labyrinths (and other labyrinths) can be expanded by inserting a spiral in the centre as shown here for troja 1. This labyrinth is used as the centre labyrinth segment in the big combined labyrinth in fig. ph1. In fig. e1 in section 7 a small spiral is used.

Tegning af troja 1 i rudeform og i trekantform og dets konstruktion

Fig. tr6: Troja 1, triangular

Troja labyrinths can be given other forms than the round and rectangular.

Here we see a couple of examples designed from the round form in A, keeping the original basic figure with the cross.


 

Troja 2 labyrint er skåret op og foldet ud, drejet 90°, og vi har bølgefigur C.

Fig. tr7: Troja 2, wave analysis.

Troja 2 labyrinth shown in detail A, is here cut open in B, the side pieces turned 90° out in D, the outmost side pieces turned further 90° in E. This long figure is compressed in F, the lane pattern drawn in H, turned 90° up and mirrored in J. Then it is seen that the labyrinth complies with wave figure C in fig. r1 in section 4. In the troja labyrinth lane 1 = lane 2 in the wave figure.

Fig. tr8: Troja 1, 2, 3 straightened out

The troja labyrinths have a characteristic lopsidedness at the entrance side from right to left, which is not liked by everybody. This lopsidedness can be corrected in different ways, e.g. with a small blind lane to the left, or by moving the entrance to the left corner, as it can be seen in fig. tr1 and tr4 above and in fig. e1, e2, and e3 in section 7. The lopsidedness can also be straightened out by “stretching” the left side a little as done here. By this the characteristic starting figure with a cross in the centre is altered. See also the straightened troja labyrinths in fig. e5 in section 7.

 

 

Troja 1½ , 2½ etc.

By leaving out angles or including angles and dots other troja type labyrinths “in between” those shown here can be made. Between troja 1 and troja 2 there can be made 14 different labyrinths and between troja 1 and troja 3 the number is 78 new labyrinths, all with the troja cross in the centre + 4 dots in the corners + from 1 to 7 corner angles. Many of these labyrinths do not comply with the labyrinth rules given by experts. One example of such a small labyrinth is given in fig. ph6 for the purpose of a philosophic consideration and for illustrating that the word labyrinth originally means dance lane.

 

 

Contents of the other sections:

 

0    Labyrinths, summary

1    Labyrinths, introduction

3    Roma-Piadena Labyrinth

4    Labyrinths of roma style

5    Chartres Labyrinth in Chartres

6    Labyrinths of chartres style

7    Comparing labyrinth-examples