三维Julia集的控制

Control of 3D Julia Sets

通过对四元数动力系统的状态变量作矩阵变换,实现了系统所生成的三维Julia集的整体缩放、沿坐标轴的放大、缩小以及错切旋转等仿射变换,并从理论上证明了通过变换后的动力系统的Julia集的拓扑性质并没有发生变化。该方法克服了对图像仿射变换所产生的图像分辨率降低的缺点,对生成高分辨率图像提供了简便可靠的方法。

Proper matrix transformations are applied to quaternion dynamical systems. The whole magnification, minification, extension along the axes and the general affine transformations including sheering and rotational transformation of 3D Julia sets generated by the quaternion dynamical systems are realized. It is also shown that the Julia sets of the transformed dynamical systems preserve the same topological properties. The proposed method solves the disadvantage of image resolution decrease and provides a simple and reliable approach to generate high resolution image.