Dual fractals

This paper presents some definitions and propositions concerning to dual fractals. Among them, dual-similarity plays a key-role not only in generating dual fractals but also in handling inter-pattern relations. Dual-similarity is basically defined as a pair of the similarity relations between two patterns, from which two mirror operators have been derived. This paper shows that each mirror operator is nothing but a contraction mapping associated with a unique attractor. Next, the mirror operator has been extended to ring mapping defined as a cyclic sequence of contraction mappings for a sequence of patterns. Basic experiments have been carried out, correlating with some application schemes, to verify the obtained theoretical outcomes in the sense of approximation to the truth.