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Zhang Fractals Yielded via Solving Time-Varying Nonlinear Complex Equations by Discrete-Time Complex-Valued ZD

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Artificial Intelligence and Computational Intelligence (AICI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7530))

Abstract

In this paper, new fractals, termed Zhang fractals, are yielded by using the discrete-time complex-valued Zhang dynamics (DTCVZD) to solve time-varying nonlinear equations in the complex domain. Such a DTCVZD model is designed by zeroing an indefinite complex-valued error function. Such Zhang fractals generated by the DTCVZD model are quite different from the famous fractals generated by Newton iteration (i.e., Newton fractals) which solves static equations. The presented DTCVZD model with different types of activation functions usable can be seen as a new iterative algorithm to produce fractals. In addition, by comparing the area and degree of blue color in Zhang fractals under the same conditions, the effectiveness of the DTCVZD model using different activation functions for solving time-varying nonlinear complex equations is reflected.

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Author information

Authors and Affiliations

  1. School of Information Science and Technology, Sun Yat-sen University, Guangzhou, 510006, China

    Yunong Zhang, Long Jin, Zhijun Zhang, Lin Xiao & Senbo Fu

Authors
  1. Yunong Zhang
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  2. Long Jin
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  3. Zhijun Zhang
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  4. Lin Xiao
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  5. Senbo Fu
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Editor information

Editors and Affiliations

  1. School of Computer and Information Engineering, Shanghai University of Electric Power, 200090, Shanghai, China

    Jingsheng Lei

  2. Deaprtment of Business Administration, Caritas Institute of Higher Education, 18 Chui Ling Road, Tseung Kwan O, Hong Kong, China

    Fu Lee Wang

  3. School of Business Information Technology and Logistics, RMIT University, City Campus, 124 la Tobre Street, 3000, Melbourne, Victoria, Australia

    Hepu Deng

  4. School of Electronics and Information, Tongji University, 201804, Shanghai, China

    Duoqian Miao

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© 2012 Springer-Verlag Berlin Heidelberg

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Zhang, Y., Jin, L., Zhang, Z., Xiao, L., Fu, S. (2012). Zhang Fractals Yielded via Solving Time-Varying Nonlinear Complex Equations by Discrete-Time Complex-Valued ZD. In: Lei, J., Wang, F.L., Deng, H., Miao, D. (eds) Artificial Intelligence and Computational Intelligence. AICI 2012. Lecture Notes in Computer Science(), vol 7530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33478-8_74

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  • DOI: https://doi.org/10.1007/978-3-642-33478-8_74

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33477-1

  • Online ISBN: 978-3-642-33478-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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