FPGA realization of fractals based on a new generalized complex logistic map. (July 2022) - Mohamed, Sara M.; Sayed, Wafaa S.; Said, Lobna A.; Radwan, Ahmed G.
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.