Application of Computer Graphics with Truncated Trigonometric Series

Abstract

In the visualization of nonlinear dynamic systems with computer, we construct the planar symmetry dynamic systems with truncated trigonometric series by Clifford A.Reiters method of constructing crystallographic groups. To analyze the characteristics of the iteration mapping with truncated trigonometric series. It used the operation of matrix product as tool. To construct dynamic systems of the nonlinear function with truncated trigonometric series. We construct two planar dynamic systems with truncated trigonometric series. Monte Carlo method is used to search the parameter vectors in the parameter space. The Lyapunov exponent is used to judge the characteristics of dynamical systems. We construct chaotic graphics in the cyclic windows. We present a method to construct symmetry dynamical systems which can be used to generate square plane tiling. A great of chaotic attractors in the fundamental regions can be continuously tiled without gaps in the plane. Furthermore, we can provide a plenty of material with a novel and unique structure for the decorative patterns of the buildings.