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Application of Fixed Point Iterative Methods to Construct Fractals and Anti-fractals

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Metric Fixed Point Theory

Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

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Abstract

In the present chapter, we demonstrate an application of fixed point iterative methods to construct fractals (Mandelbrot and Julia sets) and anti-fractals (tricorns, multicorns and Anti-Julia sets) for the complex polynomials and antipolynomials of the type \(F_{d}(z) = z^{n}+d\) and \(A_{d}(z)=\bar{z}^{m}+d\), respectively, where \(d\in \mathbb {C}\) and \(n,m\ge 2\). We derive some escape criteria to generate fractals and anti-fractals by adopting the Suantai type iterative method. Moreover, we graphically visualize and examine the dynamics of these fractals and anti-fractals for certain complex polynomials and antipolynomials, respectively. Several beautiful aesthetic patterns have been obtained which explore the geometry of fractals and anti-fractals and therefore enrich the theory of fixed points.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Government College for Girls Sector 14, Gurugram, 122001, India

    Sudesh Kumari

  2. Department of Mathematics, Government College Baund kalan, Charbhi Dadri, 127025, India

    Ashish Nandal

  3. Department of Mathematics, Maharshi Dayanand University, Rohtak, 124001, India

    Renu Chugh

Authors
  1. Sudesh Kumari
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  2. Ashish Nandal
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  3. Renu Chugh
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Corresponding author

Correspondence to Ashish Nandal .

Editor information

Editors and Affiliations

  1. Department of Applied Science and Humanities, Assam University, Silchar, India

    Pradip Debnath

  2. Department of Mathematics, Birjhora Mahavidyalaya, Bongaigaon, India

    Nabanita Konwar

  3. Faculty of Mechanical Engineering, University of Belgrade, Belgrade, Serbia

    Stojan Radenović

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Kumari, S., Nandal, A., Chugh, R. (2021). Application of Fixed Point Iterative Methods to Construct Fractals and Anti-fractals. In: Debnath, P., Konwar, N., Radenović, S. (eds) Metric Fixed Point Theory. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-16-4896-0_13

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