@article{Tassaddiq2025, 
author = {Asifa Tassaddiq and Muhammad Tanveer and Muhammad Arshad and Rabab Alharbi and and Ruhaila Md Kasmani},
title = {Fractal generation and analysis using modified fixed-point iteration},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {9462-9492},
keywords = {fixed-points, iterative methods, Mandelbrot and Julia sets, non-escape area index, average escape time, fractal dimension},
url = {https://www.sciopen.com/article/10.3934/math.2025437},
doi = {10.3934/math.2025437},
abstract = {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.}
}