abstract: In 1970, David and Knuth introduced a notation of “revolving sequences” and proved that every non-zero Gaussian integer m+in has exactly four revolving representations. In this talk, we show a close relationship between self-similar sets on the complex plane and revolving sequences. The talk will be presented with many computer graphics, and a few open problems will be introduced as well. This is joint work with Drew Allen (PhD student, UNT).