Firstly the recognition of fractal is very modern, they have only formally been studied in the last 10 years compared to Euclidean geometry which goes back over 2000 years. Fractal shapes are self similar and independent of size or scaling. Third, Euclidean geometry provides a good description of man made objects whereas fractals are required for a representation of naturally occuring geoemtries. It is likely that this limitation of our traditional language of shape is responsible for the stiking difference between mass produced objects and natural shapes. Finally, Euclidean geometries are defined by algebraic formulae, for example defines a sphere.
Fractals are normally the result of a iterative or recursive construction or algorithm.
A brief description of an 0L system will be presented here but for a more complete description the user should consult the literature. Recent usage of L-Systems is for the creation of realistic looking objects that occur in nature and in particular the branching structure of plants. One of the important characteristics of L systems is that only a small amount of information is required to represent very complex objects. Instead of working with lines as in L systems, IFS replaces polygons by other polygons as described by a generator. On every iteration each polygon is replaced by a suitably scaled, rotated, and translated version of the polygons in the generator.