Abstract

Complex graphics of nonlinear dynamical systems perform vital role in many fields, e.g., image compression or encryption, art, science, and so on. Antifractals are generated by applying a map recursively to an initial point in complex plane that have become a significant area of research these days. The purpose of this paper is to investigate the dynamics of antifractals like anti-Julia sets, tricornsand multicorns of antiholomorphic polynomials via CR iteration scheme with s-convexity. Many beautiful aesthetic patterns are visualized for antipolynomial z → z m + c of complex polynomial z m + c, for m ≥ 2 to explore the geometry of antifractals.

Highlights

  • Fractal art is generally established with the help of fractalgenerating software, iterating in three steps: correct setting of parameters; executing desirable calculation and figure out the product

  • The dynamics of antiholomorphic complex polynomials z → zm + c for m ≥ 2 with a single critical point leads to fascinating tricorns and multicorns antifractals [4]

  • MAIN RESULTS The escape criterion is important to generate the antifractals which is at the core of different applications in image encryption and computer graphics [31]

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Summary

Introduction

Fractal art is generally established with the help of fractalgenerating software, iterating in three steps: correct setting of parameters; executing desirable calculation and figure out the product. Graphics tools are used to further modify the produced patterns. The Julia and Mandelbrot sets can be recognized as symbol of fractal art [1]. It was considered that without computer fractal art could not have been organized because it provided extraordinary calculative capabilities [2]. Fractals are created by utilizing iterative methods to solve polynomial equations or non-linear equations. Generating fractals can be a mathematical model, an artistic endeavor, or just a soothing diversion. The dynamics of antiholomorphic complex polynomials z → zm + c for m ≥ 2 with a single critical point leads to fascinating tricorns and multicorns antifractals [4]

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