The Research on Strange Attractor Visualization Based on Phase- Density
基于相密度的混沌吸引子可视化方法研究

This paper puts forward the definition of phase density to quantificationally describe how the attractor distributes in the phase space, which provides effective foundation and control for strange attractor visualization. The phase density can be calculated as the proportion of the number of phase points fallen into the vessel box which is positioned around each phase space point, thus clearly denote the denseness of attractor distribution around that point. Based on the phase density, the volume rendering and Lyapunov spectra rendering of strange attractor visualization can unveil the total chaotic behavior and local attributes of strange attractor respectively. During the attractor volume visualization, the source instension and the attenuation coefficient are both defined as nonlinear component according to the average phase density, and the image ordered algorithm is adopted to reduce the expensive computation. During the Lyapunov spectra visualization, the initial iterative point pair is first picked up automatically according to the phase density, and the adaptive growing up algorithm of flow pipe (or flow ribbon) can be implemented recursively from each initial point pair. The given typical strange attractor visualization examples demonstrate that the content and form of strange attractor visualization are enriched with the complexity is depressed.