Generation of Fractals and antifracals via Hybrid Picard Noor Iteration

Abstract

Fractals are intricate, infinitely detailed formations with different scales of self-similarity, have long captivated both mathematicians and artists due to their intricate beauty and underlying simplicity. Julia sets and Mandelbrot sets are two of the most well-known types of fractals, characterized by their elaborate boundaries and recursive nature. Multicorns, a generalization of the Mandelbrot set, extend this complexity even further. In this research, we incorporate the Picard Noor iterative method, which blends aspects of Picard iteration and Noor iteration schemes. By applying this novel approach, we aim to generate visually striking and mathematically significant fractal and antifractal images, offering new insights into their geometric properties and potential applications in various scientific fields. To demonstrate the intricate architecture and visual appeal of the Julia, Mandelbrot and Multicorn Sets, we offer graphical examples.