A study of the representation of fractal curves by L systems and their equivalences

Abstract

To represent fractals by means of L systems, a graphic interpretation of the L system is required. Two families of graphic interpretations have been used: turtle graphics and vector graphics. Both are proved to be equivalent for two interesting families of L systems that include many of the fractals in the literature. The equivalence theorems make it possible to start from one L system in one of the families and obtain other systems that represent the same fractal. Sometimes a fractal that has previously been assumed not to be representable by any L system in one of the families can be shown to be representable in this way. Another point shown is the fact that supposed deficiencies in L systems, which have prompted the proposal of extensions, are really deficiencies in the graphic translation scheme.