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Fractals through modified iteration scheme. (English) Zbl 1461.37048

Summary: In this paper we study the geometry of relative superior Mandelbrot sets through \(S\)-iteration scheme. Our results are quit significant from other Mandelbrot sets existing in the literature. Besides this, we also observe that \(S\)-iteration scheme converges faster than Ishikawa iteration scheme. We believe that the results of this paper can be inspired those who are interested in creating automatically aesthetic patterns.

MSC:

37F46 Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
28A80 Fractals
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