Deterministic and Heuristic Analysis of Two-Dimensional Iterated Function Systems

Abstract

Iterated function systems offer a framework for generating complex, self-similar patterns through the iterative plotting of points. An iterated function system is a family of functions that map R^2 to R^2. For each iteration of the system, a variation is chosen with a certain probability. The asymptotic points make up the final fractal image. In this work, we examine specific variations using various heuristics that measure behavior between iterations and reveal the system's deeper patterns that improve our understanding of the system's intrinsic behavior. Our research focuses on developing and applying a multitude of heuristics designed to analyze the dynamic behavior of individual variations within these systems. Through visualizations produced by each heuristic, we illustrate the distinct characteristics of each heuristic across multiple variations.