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

Abstract

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.