FPGA REALIZATION OF COMPLEX LOGISTIC MAP FRACTAL BEHAVIOR

Abstract

This paper studies the capability of digital architecture to mimic fractal behavior. As chaotic attractors realized digitally had opened many tracks, digital designs mimicking fractals may ultimately achieve the same. This study is based on a complex single-dimensional discrete chaotic system known as the generalized positive logistic map. The fractals realized from this system are linked to the results of the mathematical analysis to understand the fractal behavior with different variations. A digital hardware architecture manifesting the fractal behavior is achieved on FPGA, showing a fractal entity experimentally. With this digital realization, it is hoped that fractals can follow the example of chaotic attractors digital applications.