Sierpinski Triangles in Stone on Medieval Floors in Rome

On the floors of churches in Rome, dating from the 11th century, a particular design can be recognized, much similar to what we today call the Sierpinsky triangle. Such floors are in opus alexandrinum, i.e. in pieces of stone of different sizes cut into the desired shape. The question then arises on the elementary shapes, their size and their lay out plan, or composition rules. Multi-scale composition is typical of the floors of the Marmorari Romani, loosely known as Cosmati, that naturally point to a fractal analysis. We found that a particular composition is present in several of these floors, more explicitly recognizable as what we today call a Sierpinsky Triangle, i.e. a subdivision on finer and finer scale of self-similar triangles. The composition is either isolated in the floors on red porphyry disc, or weaved into lattices. The instances of Sierpinsky triangles we find are all at least iterated up to three levels.