Translator Disclaimer
16 June 1995 Unification of two fractal families
Author Affiliations +
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);


Lossless adaptive differential coding of images
Proceedings of SPIE (March 02 1995)
Fractal equations and their solutions
Proceedings of SPIE (June 09 1993)
Continuous-tone image recognition using fractal theory
Proceedings of SPIE (November 30 1993)
Extensions of fractal theory
Proceedings of SPIE (August 18 1993)
Solution of fractal equation
Proceedings of SPIE (March 02 1995)
Unification of several image compression methods
Proceedings of SPIE (May 31 1994)

Back to Top