Heredity in one-dimensional quadratic maps

In an iterative process, as is the case of a one-dimensional quadratic map, heredity has never been mentioned. In this paper we show that the pattern of a superstable orbit of a one-dimensional quadratic map can be expressed as the sum of the gene of the chaotic band where the pattern is to be found , and the ancestral path that joins all its ancestors. The ancestral path h olds all the needed genetic information to calculate the descendants of the pattern. The ancestral path and successive descendant generations of the p attern constitute the family tree of the pattern, which is important to stu dy and understand the orbit's ordering. [S1063-651X(98)04212-3].