Abstract
The aim of this paper is to modify the Jungck-S iterative scheme by adding the idea of $s$ -convexity. We define and analyze the modified Jungck-S orbit (MJSO) with $s$ -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.
Highlights
In many fields of social sciences like complex graphics, biology, mathematics, computer and physics, fractal geometry plays an important role
The complex graphical behavior of fractals discussed for complex polynomial zp + c, where p ≥ 2, in orbits of one-step, two-steps and higher-steps iterations which is the application of fixed point theory in fractal geometry
GENERATION OF FRACTALS Here we demonstrate some complex graphs of Julia sets, Mandelbrot sets and biomorphs in improved Jungck-S orbit with the help of algorithms established in Sec
Summary
In many fields of social sciences like complex graphics, biology, mathematics, computer and physics, fractal geometry plays an important role. The used of implicit iteration schemes in the visualization of fractals studied in [8], Nazeer et al [9] proved new escape criterion for generalized Jungck iterations. A mistake made by Pickover in Julia sets algorithm [14] caused the appearance of biomorphs in fractal geometry. In 2016, Gdawiec et al [18] studied some generalizations of the biomorphs generation algorithm established the Pickover by using some modified iterative schemes by choosing R ∈ R+ as threshold.
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