Construction and analysis of Quaternion fractal set in a Simplex space

With our work, we take use of escape-time algorithm to construct a series of M-J sets and make an estimate of the boundary of the M set of the Quaternion based on the characteristics of Quaternion in a high dimensional dynamic space. We calculated the corresponding relationship between 4-D Bannach space & 3-D Euclid space through projection transform in Simplex coordinate system and use that relationship to get the mapping of the M-J set of Quaternion in a 3-D space. Our effort provided a constructive attempt and glimpse at the research & development of fractal theory in the multidimensional dynamic space.