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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© 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
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