Automatic Generation of 3-D Linear Fractal Shapes with Quadratic Map Basins Animation

Abstract

Quadratic map basins is a method used to generate the images of Julia and Mandelbrot sets and has been applied to visualize the attractors of iterated function systems (IFS). Three dimensional extension of such mapping with animation is an aspiring goal and a challenging task. In this paper an extension algorithm of quadratic map basin for classifying points in the complement of a 3-D linear fractal shapes are discussed. Such extension produces fractal surfaces that exhibit self-similarity and suggest smooth evolution under animation. The proposed technique has fast computations and simple representation whereby a computer can automatically select parameters and generate a large collection of aesthetically appealing 3-D fractal patterns. The simple representation and the speed of computation of our algorithm make 3-D fractal patterns reliable for interactive machine.