Fast Visualisation and Interactive Design of Deterministic Fractals

Abstract

This paper describes an interactive software tool for the visualisation and the design of artistic fractal images. The software (called AttractOrAnalyst) implements a fast algorithm for the visualisation of basins of attraction of iterated function systems, many of which show fractal properties. It also presents an intuitive technique for fractal shape exploration. Interactive visualisation of fractals allows that parameter changes can be applied at run time. This enables real-time fractal animation. Moreover, an extended analysis of the discrete dynamical systems used to generate the fractal is possible. For a fast exploration of different fractal shapes, a procedure for the automatic generation of bifurcation sets, the generalizations of the Mandelbrot set, is implemented. This technique helps greatly in the design of fractal images. A number of application examples proves the usefulness of the approach, and the paper shows that, put into an interactive context, new applications of these fascinating objects become possible. The images presented show that the developed tool can be very useful for artistic work.