As well as the square, architects used the pentagon, the octagon and the decagon (all of them constructible using a ruler and a compass) to represent, by means of accurate geometric relations, the floor plans and elevations of their constructions (Simon ).
The square, as well as the octagon, stemmed from geometries which took the heavenly Jerusalem as a model.
The style of architecture we now call Gothic first emerged between the 12th and 15th centuries of the medieval period.
It emphasized structural lightness and illumination of the inside naves.
There, the architect abandoned entirely the use of the tribune gallery and introduced the use of simple ribbed vaults.
From the 13th century onward, after these first trials, the Gothic style entered its classical stage.
Inspired by Mandelbrot’s work, Bechhoefer and Bovill used the concept of fractal dimension in architectural drawings (Bechhoefer and Bovill ) used similar techniques to analyze the design of certain architects such as Le Corbusier, Frank Lloyd Wright, Peter Eisenman and Eileen Gray.
Specifically, those authors looked for a relation between the structure of the architects’ constructions and the natural or artificial environment where those constructions were projected.
Nonetheless, the most perfect proportion stems from the pentagon and the decagon, leading to the golden ratio phi (Fig. As well as the Euclidean elements, however, there is another complex concept in the construction of the Gothic cathedrals: the unevenness of their structures, which determines their space-filling ability, i.e. The best tool to describe this concept is given by Fractal Geometry through a ratio called The aim of our investigation is to analyse the geometry of the French Gothic cathedrals in order to show the existence of a general fractal pattern.
We are not comparing the constructive processes of the cathedrals nor the will of the architects to implement their designs.