Graphs of the single-step operator for first-order logic programs — displayed in the real plane — exhibit self-similar structures known from topological dynamics, i.e. they appear to be fractals, or more precisely, attractors of iterated function systems. We show that this observation can be made mathematically precise. In particular, we give conditions which ensure that those graphs coincide w...

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-syst...

This paper discusses one method of producing fractals, namely that of iterated function systems. We first establish the tools of Hausdorff measure and Hausdorff dimension to analyze fractals, as well as some concepts in the theory of metric spaces. The latter allows us to prove the existence and uniqueness of fractals as fixed points of iterated function systems. We discuss the connection betwe...

This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function systems which depend continuously on a parameter when the space of holomorphic iterated function systems is endowed with the λ-topology. This classification...

This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function systems which depend continuously on a parameter when the space of holomorphic iterated function systems is endowed with the λ-topology. This classification...