Inversion Fractals and Iteration Processes in the Generation of Aesthetic Patterns

Abstract

In this paper, we generalize the idea of star‐shaped set inversion fractals using iterations known from fixed point theory. We also extend the iterations from real parameters to so‐called ‐system numbers and proposed the use of switching processes. All the proposed generalizations allowed us to obtain new and diverse fractal patterns that can be used, e.g. as textile and ceramics patterns. Moreover, we show that in the chaos game for iterated function systems—which is similar to the inversion fractals generation algorithm—the proposed generalizations do not give interesting results.In this paper, we generalize the idea of star‐shaped set inversion fractals using iterations known from fixed point theory. We also extend the iterations from real parameters to so‐called ‐system numbers and proposed the use of switching processes. All the proposed generalizations allowed us to obtain new and diverse fractal patterns that can be used, e.g. as textile and ceramics patterns. Moreover, we show that in the chaos game for iterated function systems—which is similar to the inversion fractals generation algorithm—the proposed generalizations do not give interesting results.