单纯形空间中的四元数分形集的构造与分析

Construction and Analysis of Quaternion Fractal Set in a Simplex Space

应用逃逸时间算法,在高维动力空间中利用四元数及其性质构造了一系列Mandelbrot和Julia集,并对四元数M集的界做出了估计·通过单纯形坐标体系下的投影变换,得到了四维Bannach空间与三维Euclid空间的对应关系,并应用这一对应关系得到了四元数M集与J集在三维空间中的映像·为分形理论在多维动力系统的研究与发展,提供了一个有益的探讨和尝试·

Uses the escape-time algorithm to construct a series of M-J sets and estimates the boundary of the M set of the quaternion, based on the characteristics of quaternion in higher dimensional dynamic space. The corresponding relationship between 4-D Bannach space and 3-D Euclid space is given through a projection transform in simplex coordinate system and, further, the relationship is used to get the mapping of the M-J set of quaternion in a 3-D space. A constructive exploration and trial pre thus provided for the research and development of fractal theory in multidimensional dynamic space.