Fractals everywhere
Fractals for the classroom. Part 1.: Introduction to fractals and chaos
Fractals for the classroom. Part 1.: Introduction to fractals and chaos
Fractal modeling of natural terrain: analysis and surface reconstruction with range data
Graphical Models and Image Processing
Optimization by Vector Space Methods
Optimization by Vector Space Methods
IEEE Transactions on Visualization and Computer Graphics
Fractal-Based Description of Natural Scenes
IEEE Transactions on Pattern Analysis and Machine Intelligence
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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.