Abstract:
The visual beauty, self-similarity, and complexity of Mandelbrot sets and Julia sets have made
an attractive eld of research. One can nd many generalizations of these sets in the literature. One such
generalization is the use of results from xed-point theory. The aim of this paper is to provide escape
criterion and generate fractals (Julia sets and Mandelbrot sets) via CR iteration scheme with s-convexity.
Many graphics of Mandelbrot sets and Julia sets of the proposed three-step iterative process with s-convexity
are presented. We think that the results of this paper can inspire those who are interested in generating
automatically aesthetic patterns.
