6. Labyrinths of chartres style

 

The most characteristic about the Chartres Labyrinth in Chartres from year 1200 is the narrow tongs of 90 and 180 length that meet at the quadrant lines 90, 180, and 270.

 

Chartres principle

A labyrinth of the chartres style should comply with the following rules

  • it has narrow tongs 90 and 180 long
  • there is symmetry in the quadrant lines 90, 180, and 270
  • there are 2, 1, or 0 radial lanes in 0 and only here

 

Square and circular

The labyrinth can be circular, square, or rectangular or of other forms. The size of the area in the centre is according to need.

We will here consider some examples of labyrinths of the chartres style. They will be smaller than the big true Chartres Labyrint in Chartres.

The figures are orientated with 0 and 90 as in mathematics, and walking the lane from outside begins with the part of the labyrinth on the left hand.

 

Symbols and units:

See the section on labyrinths in roma style.

 

 

Contents for figures:

 

Fig. ch1: Chartres systems

Fig. ch2: ch3 system in Si8-2 and Si9-3

Fig. ch3: ch5R1, ch5R2, and ch5 in Si12-2 and Ci12-2 etc.

Fig. ch4: ch6R and ch8C in e.g. Si15-3, Ci14-2, Si18-2, Ci18-2

Fig. ch5: ch10R and ch10 in Si24-4 and Si22-2

Fig. ch6: ch8E and ch8F in Ci18-2, Ci18-2, and Si20-4

Fig. ch7: ch5F as multiple choice labyrinth in Si12-2 and Ci12-2

Fig. ch8: Comparison between chartres ch5R1 and roma S13-3


 

Tegning af 13 chartres systemer fra ch3 til ch10

Fig. ch1: Chartres systems

 

We here see some proposals for labyrinths according to the chartres principle. These labyrinths are all smaller than the original labyrinth in Chartres (which is ch11).

For the clearness the labyrinths are here shown in rectangular symbolic form. Labyrinths bigger than the original Chartres are obtained by combination and extension. See also the extended Chartres labyrinth in fig. C4.

 

ch3R is the smallest labyrinth. It is 3 lanes wide, and has 1 radial lane from the edge to the centre area.

ch5R is an extension of ch3. With an additional 90 tong in each quadrant as shown we get ch5R1, or with 2 tongs 180 we get ch5R2. With additional extension with 90 tongs and 180 tongs we can get ch7R systems and ch9R systems etc. which is not shown here.

ch6R is made by combining ch3R and mirrored ch3R.

ch8R is made by combining ch3R and mirrored ch5R2.

ch9R is made by combining ch6R and mirrored ch3R.

ch10R is made by combining ch5R2 and mirrored ch5R2.

ch8C is made by combining mirrored ch3R and ch5R2. Radial lane can have a sharp bend.

ch10C is made by combining mirrored ch5R2 and ch5R2.

ch8E is made by combining ch3R and ch5R2.

ch10E is made by combining ch5R2 and ch5R2.

ch5 is made from ch5R2 by mirroring the lower 180 part and erasing the radial lane.

ch10 is made by combining ch5 and mirrored ch5.

 

The shown ch-systems can be bent to give circular labyrinths or square labyrinths or labyrinths of other forms.

ch8E and ch10E can give a circular labyrinth but not a square labyrinth because of an overlap in the radial lane crossing.

 

The 360 circle is here divided into 4 to 90, 180, 270. There can also be divided into e.g. 3 to 120 and 240 etc.

 

 

Tegning af ch3 system og kvadrat

 

 

Fig. ch2: ch3 system in Si8-2 and Si9-3

ch3 shown as square labyrinth, the smallest chartres labyrinth.

In detail B the smallest unit is a check pattern of 1. This does not give perfect symmetry of tongs by 0 quadrant line. In detail C, D, and E there is perfect tong symmetry by changing the centre square from 2 x 2 to 3 x 3 and by using a unit of where the tongs meet at 90, 180 and 270.

With a check = 1 x 1 m the lane width = 1 m total and the Si8-2 labyrinth square = 8 x 8 m with 2 x 2 m centre square as the goal.


 

Tegning af 3 stk. ch5 systemer og kvadrater

 

Fig. ch3: ch5R1, ch5R2, and ch5 in Si12-2 and Ci12-2 etc.

ch5 to square, and rectangle, and circle.

In detail D there is complete tong symmetry for ch5R1 using check unit as for ch3 above in fig. ch2.

In detail H ch5R2 is shown in rectangular form so the radial lane is in the middle of the entrance side. All the chartres labyrinths can in this easy way be stretched to rectangular form. (This can be difficult for some roma labyrinths).

ch5R1 in detail A, B, C, and D walks the 4 quadrants in turn, in partly the same way as for a roma labyrinth. But the roma should have 4 radial lanes instead of just 1. See the comparison with roma below in fig. ch8.

ch5R2 is perhaps more of chartres style than ch5R1 by moving more over 180 with alternately tongs and lines in the quadrant lines. There is symmetry of tongs in all 4 quadrant lines and symmetry between 90 and 270.

Ch5 in detail K is without radial lane in 0. By this the full symmetry by 0 is lost.

 

Tegning af ch6 og ch8 system og kvadrat

 

Fig. ch4: ch6R and ch8C in e.g. Si15-3, Ci14-2, Si18-2, Ci18-2

 

 

 

Fig. ch5: ch10R and ch10 in Si24-4 and Si22-2

In 90 and 270 there are only 2 tongs and many lines. ch10 is without radial lane in 0 and here the many tongs meet without symmetry.

 

 

Fig. ch6: ch8E and ch8F in Ci18-2, Ci18-2, and Si20-4

ch8E cannot be used as a square labyrinth because of 2 lanes crossing the same check (same flagstone). If this point is changed to make it a multiple choice labyrinth as shown in ch8F, which gives full symmetry in 0, then ch8 can also be used as square as shown in detail E.

 

Tegning af 2 stk. ch5 flervejs system og kvadrat

 

Fig. ch7: ch5F as multiple choice labyrinth in Si12-2 and Ci12-2

If you in the radial lane in ch5F1 choose to go left into lane no. 2 or into the inner lane then you just end at start again. The edge lane furthest from the centre is the right way to the centre.

ch5F2 is more symmetrical than chF1 and it is good for a special game for children (or for young people in love): You cannot catch me! In ch5F2 right after start there are 5 choices. The 2 lane to the right leads to the centre, and you are caught if someone pursues you. Try this game with your 3 year old grandchild. This labyrinth in detail F is used for the outer multiple choice chartres segment in the big combined labyrinths of fig. ph1, fig. ph2, and fig. ph4, and used in fig. ph5. See also the text of impenetrability and extricability.


Tegning af 1 stk. ch5 kvadrat og 3 stk roma S13

Fig. ch8: Comparison between chartres ch5R1 and roma S13-3.

Roma traverses each quadrant completely after turn. So does this Chartres ch5R1 though directed outwards inwards outwards inwards. Chartres has only 1 radial lane, while roma has 4 radial lanes, one in each quadrant line.

Roma in detail B has both entrance and exit at the edge. In C this is changed to have goal in the centre by just leading the exit at the edge to the centre by still another radial lane, so that there are 2 radial lanes by the entrance. This principle is seen in some classical Roman type labyrinths. Then I find the roma labyrinth in D more according to the Roma-Piadena principle, see detail A with roma basics in fig. r2.

 

 

 

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

7 Comparing labyrinth-examples