Combining complexity and harmony by the box-counting method - A comparison between entrance façades of the Pantheon in Rome and Il Redentore by Palladio

Abstract

When Benoît Mandelbrot raised the question about the length of Britain´s coastline in 1967, this was a major step towards formulating the theory of fractals, which also led to a new understanding of irregularity in nature. Since then it has become obvious that fractal geometry is more appropriate for describing complex forms than traditional Euclidean geometry (not only with regard to natural systems but also in architecture). This paper provides another view on architectural composition, following the utilization of fractal analysis. The procedure concerning the exploration of a façade design is demonstrated step by step on the Roman temple front of the Pantheon by Appolodorus and its re-interpretation - in the particular case the entrance front of Il Redentore, a Renaissance church by Palladio. Their level of complexity and range of scales that offer coherence are visualized by the specific measurement method of boxcounting.