7. Comparing labyrinth examples


Design of a labyrinth of each of the three classic types: troja, roma, and chartres, to a given square or area. (Troja and roma are classical, i.e. from ancient time; chartres is medieval).


Size of the square and area

3 squares have the sizes 10 x 10 m, 15 x 15 m, 20 x 20 m, and a circular area is 18 m in diameter. In this consideration the width of the lane is 1 m in total. On the drawings 1 check pattern is 1 x 1 m. If the width of the lane is different then e.g. 10 square means the size of 10 times the lane width. Usually all types of labyrinths are drawn according to the check pattern, which is also a rule for the roma type. But for chartres it can be an artistic advantage to use half a check pattern by the symmetry lines in some cases, and this is done here.


Favourable dimensions

The 3 types of labyrinths have their favourable dimensions, but here they have to fit into the above given dimensions.


Troja 1 has the cross dimension 7, troja 2 has cross dimension 15, troja 3 has cross dimension 23. Troja 2 and troja 3 must be ”stretched” a little to become complete squares and not rectangles. To make troja fit to 10, 20, and 18 we can add blind lanes and multiple choice lanes, the central area can be expanded or have a spiral lane added.

Roma labyrinths have some favourable square dimensions: 5, 9, 13, 17, 21, 25 etc. as seen by the figure of proposals for quadrant 4 and for quadrant 1-3 also the odd numbers in between.  So for 10, 15, 20, and 18, we must adjust the labyrinth and this can be difficult for roma. And it is not possible for all square solutions to be altered straight away to circular solutions.

Chartres is made in the same way for square and circular form. From square 12 (= e.g. ch5) and up there are solutions to all sizes, but there are though differences in how well the artistic “chartres expression” is.

Rectangular form: troja and chartres can easily be stretched to rectangular form, while it for some dimensions can be more laborious for roma.



The 3 types of labyrinths have different artistic looks:

Troja has long 360° lanes, and in some cases this will give too little mosaic appearance for a square of flagstones, and in other cases this will be the right style for the surrounding architecture. In addition there is a strong historic cultic value and tempting mystery in this ancient labyrinth also for non specialists.

Chartres has 90° and 180° lanes in a symmetrical pattern of “tongs”.

Roma has the most mosaic like possibilities for lane pattern, so that some people will not right away notice that the square pattern is a labyrinth.


Symbols and units:

See the section on labyrinths in roma style.


Contents for figures:


Fig. e1. Square 10

Fig. e2: Square 15

Fig. e3: Square 20

Fig. e4: Circle 18

Fig. e5: Troja labyrinths straightened out



Tegning af 5 stk.  kvadrat 10

Fig. e1. Square 10

Labyrinths of size 10 square: 1 troja, 3 roma, 1 chartres.

Troja: a troja 1 (= 7 square big) with 1 blind lane (+ 2) and ½ spiral in the centre (+ 1) to get a size of 10 square. At the entrance there can be a short blind lane to the left to make a complete square; or see fig. e5.

Roma: 10 is an even number so the radial lanes by the mid quadrant lines are a little displaced.

Chartres: only chartres 3 is small enough for 10 square and a centre square of 4 x 4 is then needed. (If the chartres rules are bypassed here the lane can end with a spiral to make the centre 2 x 2). Chartres labyrinths can easily be stretched to rectangular form. This is not always easy for roma labyrinths.



Tegning af 4 stk.  kvadrat 15

Fig. e2: Square 15

Labyrinths of size 15 square: 1 troja, 2 roma, 1 chartres.

Troja: this dimension is ideal for the legendary troja 2 labyrinth = Pylos labyrinth from year -1200. The labyrinth has though to be stretched 1 at the centre cross line to change the dimension from 14 x 15 to 15 x 15. The troja labyrinth is a little lopsided from right to left by the entrance. If this look does not fit for the square it can be corrected by having a short blind lane to the left here or by moving the entrance to the left corner; or see fig. e5.

Roma: Detail B has both entrance and exit at the edge and consists of 4 identical quadrants with the most simple wave figure (wave figure B). Walking in the labyrinth you will slowly approach the “dangerous centre with the horror” and then hurry away again out along the radial lane, 4 times in all. Detail C has its goal in the centre, which is the attractive place in this labyrinth.

Chartres: A chartres 6 (i.e. 6 lanes from the centre and out) with a 3 x 3 centre square fits with 15 square.

It is seen that the troja labyrinth shows the most calm look with long straight lanes, and the roma labyrinth shows the most variegated look.

Tegning af 3 stk.  kvadrat 20

Fig. e3: Square 20

Labyrinths of size 20 square: 1 troja, 1 roma, 1 chartres.

Troja: chosen: troja 2 (= 15 big) with 1 blind lane (+ 2) and 1 multiple choice lane (+ 2) and an expansion of the centre space (+ 1), total 20.

Roma: Si20 here is designed from Si21-1rp11-1 in fig. r9 which uses waveform E and H.

Chartres: chosen ch8 multiple choice lane labyrinth with 4 x 4 centre square.



Tegning af 3 stk.  Cirkel 18


Fig. e4: Circle 18

Labyrinths of size 18 circle: 1 troja, 1 roma, 1 chartres.

Troja: chosen troja 2 (= 15 big) with blind lane (+ 2) and expanded centre place (+ 1).

Roma: chosen Si17-1rp9-1 in fig. r5 which is expanded and modified by giving bigger centre space. (These round labyrinths should be drawn more beautiful than I have done).

Chartres: 18 is a favourable dimension for chartres and we choose ch8E with its beautiful symmetry in all 4 quadrant lines.




Fig. e5: Troja labyrinths straightened out

The 4 troja labyrinths from fig. e1, e2, e3, e4 have here had their characteristic lopsidedness straightened out by “stretching” the left side a little, as shown in fig. tr8 in section 2.



See fig. ph1 for a big combined labyrinth: a chartres labyrinth with a roma labyrinth inside with a troja labyrinth inside.



Contents of the other sections:


0    Labyrinths, summary

1    Labyrinths, introduction

2    Troja labyrinths

3    Roma-Piadena Labyrinth

4    Labyrinths of roma style

5    Chartres Labyrinth in Chartres

6    Labyrinths of chartres style