Fractal Generation in Modified Jungck–S Orbit

The aim of this paper is to modify the Jungck-S iterative scheme by adding the idea of <inline-formula> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula>-convexity. We define and analyze the modified Jungck-S orbit (MJSO) with <inline-formula> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula>-convex combination and derive the escape criterion for MJSO. Moreover, we establish the algorithms to visualize some Julia sets, Mandelbrot sets, and biomorphs in this orbit. In the biomorph generation algorithm, we did not fix the threshold radius of proposed orbit (i.e., MJSO) as fixed in literature earlier. We also discuss the graphical behavior of some complex polynomials in the generation of Julia sets, Mandelbrot sets, and biomorphs in MJSO.

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