Generation of 3D Fractal Images for Mandelbrot and Julia Sets

Abstract

Fractals provide an innovative method for generating 3D images of real-world objects by using computational modelling algorithms based on the imperatives of self-similarity, scale invariance, and dimensionality. Images such as coastlines, terrains, cloud mountains, and most interestingly, random shapes composed of curves, sets of curves, etc. present a multivaried spectrum of fractals usage in domains ranging from multi-coloured, multi-patterned fractal landscapes of natural geographic entities, image compression to even modelling of molecular ecosystems. Fractal geometry provides a basis for modelling the infinite detail found in nature. Fractals contain their scale down, rotate and skew replicas embedded in them. Many different types of fractals have come into limelight since their origin. This paper explains the generation of two famous types of fractals, namely the Mandelbrot Set and Julia Set, the3D rendering of which gives a real-world look and feel in the world of fractal images.