Based on simplified Lorenz multiwing and Chua multiscroll chaotic systems, a rotation compound chaotic system is presented via transformation. Based on a binary fractal algorithm, a new ternary fractal algorithm is proposed. In the ternary fractal algorithm, the number of input sequences is extended from 2 to 3, which means the chaotic attractor with fractal transformation can be presented in the three-dimensional space. Taking Lorenz system, rotation Lorenz system and compound chaotic system as the seed chaotic systems, the dynamics of the complex chaotic attractors with fractal transformation are analyzed by means of bifurcation diagram, complexity and power spectrum, and the results show that the chaotic sequences with fractal transformation have higher complexity. As the experimental verification, one kind of complex chaotic attractors is implemented by DSP, and the result is consistent with that of the simulation, which verifies the feasibility of digital circuit implement.

Designing a discrete chaotic system via fractal transformation has become a new method for engineering applications. This method generates new discrete chaotic system through external mechanisms, instead of the traditional way of internal mechanisms. The way of building novel discrete chaotic system is enriched by fractal and mathematical operation. Taking one-dimensional ICMIC map and two-dimensional Hénon map as the seed maps, dynamics of the generated chaotic map is analyzed by bifurcations, complexity and spectrum distribution characteristics. The results show that the new discrete chaotic map has the advantages in complexity and distribution in the parameter space. Finally, the digital circuit of fractal chaotic system is implemented based on DSP technique. The feasibility of the circuit is verified. Therefore, it has good application prospects in secure communication.