We describe a flexible algorithm that can create many different kinds of aesthetic fractal patterns. The main idea of the algorithm is to randomly place progressively smaller copies of a motif within a region, thus producing a fractal pattern. This has been found to work for a wide variety of shapes for both the motif and the enclosing region. We show a several examples. If the region is a fund...

Lworld is a computer graphics animation system based on L-systems, a parallel rewriting technique used primarily in computer graphics for plant modeling. Because rule-based programming is a powerful technique, we use it as a basis for a general-purpose animation system called Lworld (LSystem world). We describe the architecture, the features, and the programming language of the animation system...

The concept of derivative coordinate functions proved useful in the formulation of analytic fractal functions to represent smooth symmetric binary fractal trees [1]. In this paper we introduce a new geometry that defines the fractal space around these fractal trees. We present the canonical and degenerate form of this fractal space and extend the fractal geometrical space to R explicitly and R ...

Previously we described an algorithm that can fill a region with an infinite sequence of randomly placed and progressively smaller shapes, producing a fractal pattern. If the algorithm is appropriately modified and the region is a fundamental region for one of the 17 “wallpaper” groups, one can obtain a fractal pattern with that symmetry group. This produces artistic patterns which have a pleas...

Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical propertie...