Generation of Julia and Mandelbrot Sets for a Complex Function via Jungck–Noor Iterative Method with s-Convexity

This paper introduces novel, non-classical Julia and Mandelbrot sets using the Jungck–Noor iterative method with s-convexity, and derives an escape criterion for higher-order complex polynomials of the form zn+ℑz3−ℜz+ω, where n≥4 and ℑ,ℜ,ω∈C. The proposed method advances existing algorithms, enabling the visualization of intricate fractal patterns as Julia and Mandelbrot sets with enhanced complexity. Through graphical representations, we illustrate how parameter variations influence the color, size, and shape of the resulting images, producing visually striking and aesthetically appealing fractals. Furthermore, we explore the dynamic behavior of these sets under fixed input parameters while varying the degree n. The presented results, both methodologically and visually, offer new insights into fractal geometry and inspire further research.