The concept of “Leaping Iterated Function Systems (LIFS in short)” is a variation of Iterated Function Systems (IFS), that originated from “self-similarity”, i.e., the whole has the same shape as one or more of the parts. The methodology of Leaping IFS is first to construct a structure of the whole by parts, then to convert it to an image, and then to replace each part with this image. Repeat the procedures until the outcome is visually satisfied. One of the key features of Leaping IFS is that computer resource consumption will be under control during the iterations because the number of parts in the whole structure is fixed.