Dynamics Motivated by Sierpinski Fractals

Abstract

Fatou-Julia iteration (FJI) is an effective instrument to construct fractals. Famous Julia and Mandelbrot sets are strong confirmations of this. In the present study, we use the paradigm of FJI to construct and map Sierpinski fractals. The fractals can be mapped by developing a mapping iteration on the basis of FJI. Because of the close link between mappings, differential equations and dynamical systems, one can introduce dynamics for a fractal through differential equations such that it becomes points of the solution trajectory. Thus, in this paper, we consider two types of dynamics motivated by the Sierpinski fractals. The first one is the dynamics of FJI itself, and the second one is the dynamics of a fractal mapping iteration which can be performed through differential equations. The characterization of fractals as trajectory points of the dynamics can help to enhance and widen the scope of their applications in physics and engineering.