Abstract
In this chapter, dynamics are constructed for fractals utilizing the motion associated with differential equations. Firstly, we introduce an algorithm to map fractals by developing a mapping iteration on the basis of Fatou–Julia iteration. 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. In the present chapter, Julia set, Mandelbrot set, and Sierpinski fractals are considered as initial points for the trajectories of the dynamics. 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.
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Akhmet, M., Fen, M.O., Alejaily, E.M. (2020). Fractals: Dynamics in the Geometry. In: Dynamics with Chaos and Fractals. Nonlinear Systems and Complexity, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-030-35854-9_11
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