Parametric 2-dimensional L systems and recursive fractal images: Mandelbrot set, Julia sets and biomorphs

Abstract

L systems have proved their expressive power. They have been used to represent the class of the initiator/iterator fractal curves (such as Sierpinski's gasket and von Koch's snowflake curve). Parametric L systems, introduced by Prusinkiewicz and Lindenmayer, link real-valued parameters to the symbols. In this paper, parametric 0L systems are extended to n dimensions and used to represent a different class of classic fractals that includes objects such the Mandelbrot and Julia sets, or Pickover's biomorphs.