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Generating Mandelbrot, Julia and Multicorn set using AH iteration

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  • Gautam, Pragati
  • Ashish,

Abstract

This paper proposes the AH iteration approach to construct Mandelbrot, Julia, and Multicorn sets, where the polynomials are of the form zq+c in the complex plane. We establish an escape criterion that has been created for the AH iteration framework. We then show graphical representations of Mandelbrot, Julia, and Multicorn sets generated using this escape criterion and the escape-time algorithm. Furthermore, we investigate how variations in iteration parameters affect the form and size of the Mandelbrot, Julia, and Multicorn sets. We also examine how the iteration parameters depend on numerical measures, which are the average escape time (AET), the non-escaping area index (NAI) and the box-counting dimension. Furthermore, we examine the nature of dependency, whether it follows a linear or non-linear pattern.

Suggested Citation

  • Gautam, Pragati & Ashish,, 2026. "Generating Mandelbrot, Julia and Multicorn set using AH iteration," Chaos, Solitons & Fractals, Elsevier, vol. 208(P2).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p2:s0960077926003589
    DOI: 10.1016/j.chaos.2026.118217
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