Escape-Time Modified Algorithm for Generating Fractal Images Based on Petri Net Reachability

This paper presents a new approach to computer image generation via three proposed methods for translating the evolution of a Petri net into fractal image synthesis. The idea is derived from the concept of fractal iteration principles in the escape-time algorithm and chaos game. The approach uses a Petri net as a powerful abstract modeling tool for fractal image synthesis via its duality, deadlock, inhibitor arc, firing sequence and marking reachability. The objective of this approach is to enhance the analysis technique of a Petri net and use it as a novel technique for fractal image synthesis. Generating fractal images via the dynamics of a Petri net allows an easy and direct proof for the similarity and correspondence between the dynamics of complex quadratic fractals by the recursive procedure of the escape-time algorithm and the state of a Petri net via a reachability problem. The reachability problem will be manipulated in terms of the dynamics of the fractal in order to generate images via three proposed methods. Validation of our approach is given by discussion and an illustration of some experimental results. key words: escape-time algorithm, reachability problem, Petri net, chaos game, iterated function system, PN duality