FPGA realization of fractals based on a new generalized complex logistic map. (July 2022)

• Record Type: Journal Article
• Authors: Mohamed, Sara M.; Sayed, Wafaa S.; Said, Lobna A.; Radwan, Ahmed G.
• Is Part Of: Chaos, solitons and fractals. Volume 160(2022)
• Publication Date: 2022-07
• Subjects: Chaotic systems -- FPGA -- Fractals -- Logistic map; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112215
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: This paper introduces a new generalized complex logistic map and the FPGA realization of a corresponding fractal generation application. The chaotic properties of the proposed map are studied through the stability conditions, bifurcation behavior and maximum Lyapunov exponent (MLE). A relation between the mathematical analysis and fractal behavior is demonstrated, which enables formulating the fractal limits. A compact fractal generation process is presented, which results in designing and implementing an optimized hardware architecture. An efficient FPGA implementation of the fractal behavior is validated experimentally on Artix-7 FPGA board. Two examples of fractal implementation are verified, yielding frequencies of 34.593 MHz and 31.979 MHz and throughputs of 0.415 Gbit/s, 0.384 Gbit/s. Compared to recent related works, the proposed implementation demonstrates its efficient hardware utilization and suitability for potential applications.