Owen Jones in The Grammar of Ornament clearly states that ornament comes from a deep observation of nature. He emphasizes the importance of the harmony of the parts and the subordination of one part to another. This subordination and harmony between the parts is what fractal geometry explores as self-similarity and self-affinity. An iterated function system (IFS) is a digital method of producing fractals. An IFS in the shape of columns holding up a lintel produced an attractor displaying fluted columns with capitals and an entablature with the proper number and spacing of triglyphs and mutules. Thus, fractal geometry, through the use of iterated function systems, provides a new insight into the intention of Doric ornament design.