Maze Layout

This page was last updated on 17th January 2009.

Classification

Type	Details	Mazes
Tangential-radial	Single standard	Guingamp
	Double standard	Wing
		Alkborough
		Alkborough Church
		Hilton (variant)
		Whitfield Place (variant)
		Breamore
		St. Mary Redcliffe
		Victoria Park
		Chartres
		St. Quentin
		Amiens
		Poitiers (variant)
		Mirepoix (variant)
		Sélestat
		Lucca
		Cologne
		Maastricht
	Triple standard	Saffron Walden
	¼,¼,3(½,¼), ¼,1,¼,¼,½,½,1, ½,¼,½,¾,¼,¼; I3,2O,2I,2O,8I,4O,2I,I3.	Winchester
	2(1,¼,¼,½,¼, ½,¼,½,¼,¼,1); I5,3O,2I,2O,2I,O3,I5,3I,2O,2I,2O,I3,I.	Bayeux
	¼,¼,2(½,¼,¾),¼,¼, 3(½,¼),3(¼); I7,2O,2I,6O,2I,2O,4I,I3.	Ravenna
	4(9(¼)+); I9,3(2(O3,I,I,O3),I8),2(O,O3),I,2(I,I3)).	Piadena
	10(1); I7,O5,I3,2O,I3,O5,I7,I,O9.	Hannover
	11(1); 2(I5,O3,2I,O3,I5).	Graitschen (variant)
	11(1); 2(I5,O3,2I,O3,I5).	Steigra
	7(1); 2(I3,O,O,I3).	Skewsby
Cartesian cruciform		Chambéry
		St. Omer
		Ghent
Other		Ely

Types

Tangential-radial

Mazes belonging to this type have the following features.

The path consists entirely of alternating radial and tangential segments.
The tangential segments alternate between clockwise and anticlockwise (with rare exceptions).
The path never crosses the line between the entrance and the centre.

Cartesian cruciform

Mazes belonging to this type have the following features.

The path fits within a rectangular (cartesian) grid.
The entrance is in the middle of one side.
On the opposite side of the centre from the entrance the path has a cruciform shape.
Between the centre and the entrance there is a single "dead" square.
The path never crosses the line between the entrance and the centre.

Details

I have used the following four-part notation to describe tangential-radial layouts. (However, in the classification on this page, I have omitted the first and fourth parts.)

"Clockwise" or "anticlockwise". This is the sense of the first tangential segment.
A sequence describing the tangential segments (in order). Each number in the sequence is the fraction of a complete circuit that the segment covers. Where there is a sequence enclosed in parentheses and preceded by a number, this means that the sequence is repeated that number of times. By default, segments are in alternating senses (clockwise and anticlockwise); a plus sign indicates instances where the sense does not alternate.
A sequence of Os and Is describing the radial segments (in order). I means "in" (towards the centre), O means "out" (away from the centre). Where an I or O is followed by a number, this means that the segment consists of that number of circuits inwards or outwards (the default is 1). Where an I or O (or sequence of Is and Os enclosed in parentheses) is preceded by a number, this means that the segment (or sequence) is repeated that number of times.
"Circular", "octagonal" or "square", which is self-explanatory.

The cartesian cruciform layout does not lend itself to this sort of analysis.

The standard layout

As the classification above shows, the double clockwise standard is by far the most common common layout. Shorn of all ornament it looks like this (the cardinal points are arbitrary).

What, if anything, is special about this design? If you imagine cutting it along a straight line from the entrance to the centre (the red line in the diagram above), and then stretching out the resulting shape into a rectangle, you will transform it into the following.

This design has three noteworthy features.

It has 180-degree symmetry about its centre. The consequence of this is that, if you walk the maze from the entrance to the centre, you will execute the same sequence of left and right turns and follow the same sequence of radial and tangential displacements as you would do if you walked the maze in the opposite direction (from the centre to the entrance). Another way of viewing this is to consider the second and third parts of the four-part notation that I have used to describe the layout. Both parts are palindromic.
It consists of two occurrences of a smaller basic unit (the green line is at the junction of the two occurrences). This is the reason why I have called this a "double" standard layout. If you carry out the same transformation on the maze at Saffron Walden (ignoring the bastions), you will find that that maze consists of three occurrences of the basic unit. And similarly Guingamp (omitting the outer circuit) consists of only one occurrence of the basic unit.
The design is "handed": that is to say, it is not the same as its mirror image. I refer to this as the "clockwise" standard layout, because in walking from the entrance to the centre you make one clockwise circuit of the centre. Only Guingamp (omitting the initial extra circuit) and Mirepoix (modified) are of the anticlockwise form.

The general formula for the second and third parts of an n-fold standard layout is:

(n - 1)(¼,¼),½,½,¼, (2n - 1)(¼,½,¼,½,¼,½,¼), ¼,½,½,(n - 1)(¼,¼).
I5,(n - 1)(I,I5),4O,4I,(n - 1)(10O,4I),4O,I5,(n - 1)(I,I5)

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