Language-Restricted Iterated Function Systems, Koch Constructions, and L-systems

1 Introduction Linear fractals can be generated using a variety of methods. This raises the question of finding equivalent methods for generating the same fractal. Several aspects of this question have been addressed in the literature. These include: A method for converting Koch constructions to equivalent iterated function systems (IFS's) [11], Methods for converting selected classes of L-systems with geometric interpretation to extensions of IFS's, such as controlled iterated function systems (CIFS's) [10] and mutually recursive function systems (MRFS's) [4]. Previous course notes [9] introduced the notion of language-restricted iterated function systems (LRIFS's) encompassing CIFS's and MRFS's, and included a number of sample LRIFS's equivalent to L-systems with turtle interpretation. The present notes include the following further extensions to these results: Introduction of the notions of iterated transformations of coordinate systems (ITCS's) and their language