Fractal design based on multi-scroll hidden attractor and its application in image encryption

Abstract

In this research, on the basis of a seed chaotic system of no equilibrium point, some novel system models that can produce multi-scroll hidden attractors are given. Particularly, the new differential equation is reconfigured to a three novel seed system. Then, on the basis of a three seed system, some fractal algorithms are designed based on a Julia set. Furthermore, the constant term of Julia fractal mapping is set to 0, and two solutions of equations are obtained. In combination with Julia set’s solution and some seed system models, some interesting fractal patterns can be obtained. In particular, based on some maps, such as a parabolic map and a triangle map, some new overlay fractal graphs are given. The study of fractal based on seed systems provides a new direction for the study of nonlinear dynamics. The encipherment scheme of high security provides feasibility for the combination of chaos, fractals, and cryptology.