The recurrent iterated function system and the L-system are two powerful linear fractal models. The main drawback of recurrent iterated function systems is a difficulty in modeling whereas the main drawback of L-systems is inefficient geometry specification. Iterative and recursive structures extend the object instancing paradigm, allowing it to model linear fractals . Instancing models render ...

Images are created using probabilistic iterated function systems that involve both affine transformations of the plane and isometries of hyperbolic geometry. Figures of attractors with striking hyperbolic symmetry are the result.

We prove that any iterated function system of finite type possesses the weak separation property.

Let I = {φj}j=1 be an iterated function system (IFS) consisting of a family of contractive affine maps on Rd. Hutchinson [8] proved that there exists a unique compact set K = K(I), called the attractor of the IFS I, such that K = ⋃m j=1 φj(K). Moreover, for any given probability vector p = (p1, . . . , pm), i.e. pj > 0 for all j and ∑m j=1 pj = 1, there exists a unique compactly supported proba...

The escape-time method was introduced to generate images of Julia and Mandelbrot sets, then applied to visualize attractors of iterated function systems. This paper extends it further to language-restricted iterated function systems (LRIFS's). They generalize the original deeni-tion of IFS's by providing means for restricting the sequences of applicable transformations. The resulting at-tractor...

The theory of iterated function systems (IFS) on complete metric spaces appears in almost all fractal based algorithms used for the purpose of compression of the images and their representation as well. Through a simple mathematical model, IFS technique provides an important tool for description and manipulation of the complex fractal attractors. In this paper we study the iterated function sys...

The escape-time method was introduced to generate images of Julia and Mandelbrot sets, then applied to visualize attractors of iterated function systems. This paper extends it further to language-restricted iterated function systems (LRIFS's). They generalize the original de nition of IFS's by providing means for restricting the sequences of applicable transformations. The resulting attractors ...

Feng and Wang showed that two homogeneous iterated function systems in R with multiplicatively independent contraction ratios necessarily have different attractors. In this paper, we extend this result to graph directed iterated function systems in R with contraction ratios that are of the form 1 β , for integers β. By using a result of Boigelot et al., this allows us to give a proof of a conje...

Before rendering 2D or 3D fractals with iterated function systems, it is necessary to calculate the bounding extent of fractals. We develop a new algorithm to compute the bounding box which closely contains the entire attractor of an iterated function system. r 2003 Elsevier Science Ltd. All rights reserved.