As early as the ninth century Muslim artists began incorporating multiple-level designs into their ornament. In time, this fascination found expression in each of the three principle areas of Islamic two-dimensional artistic expression: calligraphy, the floral idiom, and geometric pattern. In both the western regions of Morocco and Andalusia, and the eastern regions of Persia, Khurasan and Transoxiana, during the fourteenth and fifteenth centuries respectively, previously established systematic methods of two-dimensional geometric pattern construction were used in the development of three distinct traditions of self-similar geometric design. These innovations resulted in the last great advancement in the long history of Islamic geometric pattern making. Furthermore, these patterns are very likely the first, and among the most engaging, examples of complex overtly self-similar art made by man. The traditional techniques used in the creation of Islamic self-similar patterns, overviewed herein, are easily learned and open to further creative development. In addition to new and original two-dimensional periodic designs (as per historic examples), further areas of stylistically Islamic self-similar geometric pattern innovation can include their application to aperiodic tilings, as well as non-Euclidean hyperbolic and spherical surface coverage.