Davis and Knuth in 1970 introduced the notion of revolving sequences, as representations of a Gaussian integer. Later, Mizutani and Ito pointed out a close relationship between a set of points determined by all revolving sequences and a self-similar set, which is called the Dragon from the viewpoint of symbolic dynamical systems. We will show how their result can be generalized by a completely different approach. The talk will be presented with a lot of pictures; accessible for graduate students. A few open problems will be introduced as well. This is a joint work with Drew Allen (UNT).