Fractal generation and analysis using modified fixed-point iteration

Fractals exhibit self-similarity across scales and have significant mathematical and artistic appeal. This study proposed a modified fixed-point iteration (MFPI) to generate fractals for the complex polynomial $y^k+c$. The escape criterion for MFPI was established, enabling the construction of Mandelbrot and Julia sets. Comparative image analysis with M, Picard-Mann, and Mann iterations highlighted visual differences. Numerical metrics, including non-escape area index (NAI), average escape time (AET), fractal dimension (FD), and execution time, assessed the efficiency and performance of MFPI against existing methods.