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Analysis and FPGA of semi-fractal shapes based on complex Gaussian map

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  • AboAlNaga, BahaaAlDeen M.
  • Said, Lobna A.
  • Madian, Ahmed H.
  • Radwan, Ahmed G.

Abstract

This paper studies the fractal-like behavior exhibited by the complex form of Gaussian chaotic map and the capability of digital architectures to mimic that behavior. Digitally realized chaotic attractors had many applications; hopefully, a digital realization of fractals may achieve the same eventually. The Gauss map is viewed concerning its bifurcation behavior, time waveform plots, Lyapunov exponent, and attractor performance through parameter variation. The Fractal-like entities emerging from the perceived complex map are examined versus different map coefficients for the highest chaotic periods to extract an interpretation for the fractal behavior. FPGA implementation of the fractal behavior is discussed viewing an optimized hardware architecture that eventually displays a fractal entity experimentally.

Suggested Citation

  • AboAlNaga, BahaaAlDeen M. & Said, Lobna A. & Madian, Ahmed H. & Radwan, Ahmed G., 2021. "Analysis and FPGA of semi-fractal shapes based on complex Gaussian map," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920308857
    DOI: 10.1016/j.chaos.2020.110493
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    References listed on IDEAS

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    1. Soliman, Nancy S. & Tolba, Mohammed F. & Said, Lobna A. & Madian, Ahmed H. & Radwan, Ahmed G., 2019. "Fractional X-shape controllable multi-scroll attractor with parameter effect and FPGA automatic design tool software," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 292-307.
    2. Ketan Jha & Mamta Rani, 2018. "Control of Dynamic Noise in Transcendental Julia and Mandelbrot Sets by Superior Iteration Method," International Journal of Natural Computing Research (IJNCR), IGI Global, vol. 7(2), pages 48-59, April.
    3. Lahmiri, Salim & Bekiros, Stelios, 2018. "Chaos, randomness and multi-fractality in Bitcoin market," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 28-34.
    4. Bouallegue, Kais & Chaari, Abdessattar & Toumi, Ahmed, 2011. "Multi-scroll and multi-wing chaotic attractor generated with Julia process fractal," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 79-85.
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    Cited by:

    1. Mohamed, Sara M. & Sayed, Wafaa S. & Said, Lobna A. & Radwan, Ahmed G., 2022. "FPGA realization of fractals based on a new generalized complex logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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