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Proceedings Paper

Unification of two fractal families
Author(s): Ying Liu
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Paper Abstract

Barnsley and Hurd classify the fractal images into two families: iterated function system fractals (IFS fractals) and fractal transform fractals, or local iterated function system fractals (LIFS fractals). We will call IFS fractals, class 2 fractals and LIFS fractals, class 3 fractals. In this paper, we will unify these two approaches plus another family of fractals, the class 5 fractals. The basic idea is given as follows: a dynamical system can be represented by a digraph, the nodes in a digraph can be divided into two parts: transient states and persistent states. For bilevel images, a persistent node is a black pixel. A transient node is a white pixel. For images with more than two gray levels, a stochastic digraph is used. A transient node is a pixel with the intensity of 0. The intensity of a persistent node is determined by a relative frequency. In this way, the two families of fractals can be generated in a similar way. In this paper, we will first present a classification of dynamical systems and introduce the transformation based on digraphs, then we will unify the two approaches for fractal binary images. We will compare the decoding algorithms of the two families. Finally, we will generalize the discussion to continuous-tone images.

Paper Details

Date Published: 16 June 1995
PDF: 13 pages
Proc. SPIE 2488, Visual Information Processing IV, (16 June 1995); doi: 10.1117/12.211985
Show Author Affiliations
Ying Liu, Savannah State College (United States)


Published in SPIE Proceedings Vol. 2488:
Visual Information Processing IV
Friedrich O. Huck; Richard D. Juday, Editor(s)

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