Why are Gothic cathedrals so enchanting? Scientists pondered this and discovered a surprising mathematical reason: a hidden pattern known as ‘fractal geometry’. Never heard of it? Neither had I, so I delved into it. After reading this blog, you’ll look at the next cathedral with new eyes!
Fascinating Cathedrals
Gothic cathedrals, built between the 12th and 16th centuries, are fascinating, and for a reason. They are famous for their architectural innovations such as pointed arches, ribbed vaults, and flying buttresses. These elements allowed for taller and lighter structures, in stark contrast to the heavy, gloomy Romanesque buildings that preceded them. Read more about this in this blog.
The Birth of Gothic Cathedrals
Gothic architecture originated in the Île de France region, under the patronage of powerful abbots and kings. The Abbey of Saint-Denis, led by Abbot Suger, is often considered the birthplace of this style (see photo). Following this pioneering project, iconic cathedrals like Notre-Dame of Paris and Chartres Cathedral were built.
The Birthplace of Gothic Architecture is in Paris
Not the Notre-Dame of Paris is the Birthplace of Gothic Architecture, but the cathedral of Saint-Denis, build by abbot Suger.
These cathedrals were not only religious centers but also technological and artistic masterpieces. Initially, construction was largely intuitive. It was pretty much ‘trial and error’: if the walls are thick enough, the building might just stand up (fingers crossed).
Around the 12th century, access to new knowledge (think geometry and logic) became available. Victories over the Moors meant French knights brought home captured writings to knowledge hubs (‘Schools’) like Paris, Chartres, and Laon. This sparked an understanding of the theoretical underpinnings of construction.
This enabled Gothic architects to adopt a more rational approach. They realized that a stable skeleton formed by columns, vaults, and buttresses was enough to support the roof’s weight. Scientific research supports the idea that the Gothic cathedral was built with geometric knowledge.
The Research: Cathedrals and Fractal Patterns
Two scientists, Albert Samper and Blas Herrera, conducted years of research on Gothic cathedrals. They discovered that the beauty and harmony of these buildings are not only the result of aesthetic choices but are also deeply rooted in mathematical principles that govern natural and artificial forms. How did they find out? By applying the concept of ‘fractal geometry’.
The researchers studied 20 remarkable French Gothic cathedrals, including those in Strasbourg, Paris, Sens, and Reims. These cathedrals were selected for their stylistic, chronological, and geographical significance, offering a representative sample of Gothic architecture.
Fractal Parameter: Measuring Complexity
To quantify the fractal nature of the cathedrals, the researchers developed a specific measure called the ‘fractal parameter’ (Ps). This parameter measures the ‘roughness’ or complexity of a structure. The higher the fractal parameter, the more intricate and detailed the structure is.
The process involved several steps. First, detailed architectural drawings were collected. These were redrawn using CAD software (Computer-Aided Design) to make them suitable for fractal analysis. Using a series of mathematical calculations, the researchers could determine the fractal parameters for each cathedral.
Fractal Geometry
Fractal Geometry is a mathematical concept developed by Benoit Mandelbrot in the 1970s. A fractal is a pattern that repeats itself at different scales. Imagine zooming in on a snowflake: the more you zoom in, the more the same complex patterns continue to appear. This is the idea of a fractal.
What Did They Discover?
The analysis revealed that French Gothic cathedrals possess a non-random fractal pattern. This means that the patterns these cathedrals follow are not by chance but rather natural or intentional repetitions at different scales.
This discovery enriches our understanding of Gothic architecture. It shows how medieval architects may have intuitively applied fractal principles long before these were formally documented in modern mathematics.
Why Is This Important?
Research into the fractal patterns in Gothic cathedrals opens new avenues for exploring historical architecture. It suggests that the beauty and harmony of these structures are based not only on aesthetic choices but also on deeply rooted mathematical principles.
For lovers of architecture and mathematics, this study offers a fascinating insight into the design strategies of medieval builders. It also helps us appreciate the intriguing balance of art, science, and spirituality that characterizes Gothic cathedrals.
Mathmatical precision
The hidden ‘fractal geometry’ of French Gothic cathedrals is a testament to the genius of their creators. It combines timeless beauty with mathematical precision. As we explore these connections further, we uncover not only the secrets of the past but also the enduring principles that shape our understanding of the world.
The next time you visit a Gothic cathedral, you might see it with different eyes. You won’t just see an architectural marvel but also gain an appreciation for the infinite possibilities of fractal geometry.
