Exploring the Julia and Mandelbrot sets of [formula omitted] using a four-step iteration scheme extended with [formula omitted]-convexity.

Iterative approaches have been established to be fundamental for the creation of fractals. This paper introduces an approach to visualize Julia and Mandelbrot sets for a complex function of the form Q (z) = z p + log c t for all z ∈ ℂ , where p ∈ N ∖ { 1 } , t ∈ [ 1 , ∞) , c ∈ ℂ ∖ { 0 } , using a four-step iteration scheme extended with s -convexity. The study introduces an escape criteria for generating Julia and Mandelbrot sets using a four-step iterative method. It investigates how changes in the iteration parameters influence the shape and color of the resulting Julia and Mandelbrot sets. This approach can generate a wide range of captivating fractals and analyze them through numerical experiments. [ABSTRACT FROM AUTHOR]