Multiple-cell elements and regular multifractals

Abstract

Based on fractal super fibers and binary fractal fibers, the following objectives are approached in this paper: First, the concept of multiple-cell elements is induced and abstracted. Second, through multiple-cell elements, the constructability of regular multifractals with strict self-similarities is confirmed, and the universality of the construction mode for regular multifractals is proved. Third, through the construction mode and multiple-cell elements, regular multifractals are demonstrated to be equivalent to generalized regular single fractals with multilayer fine structures. On the basis of such equivalence, the dimension formula of the regular single fractal is extended to that of the regular multifractal, and the geometry of regular single fractals is extended to that of regular multifractals. Fourth, through regular multifractals, a few golden fractals are constructed.