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16 June 1995 Unification of two fractal families
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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.
© (1995) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Ying Liu "Unification of two fractal families", Proc. SPIE 2488, Visual Information Processing IV, (16 June 1995); https://doi.org/10.1117/12.211985
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