Generating directional attractors based on multiple subdivision

The connection between self-similar fractals and subdivision shows that self-similar fractals can be generated as attractors by an extended family of subdivision schemes. This paper aims to equipe these attractors with directions. Such directional attractors in this paper are generated based on a kind of multiple subdivision, which owns several anisotropic subdivision operators and generate surfaces with directions. For the multiple subdivision, we derive an iterated function system for each anisotropic subdivision operator to get a multiple function system, which can be arranged in a tree structure. Then by controlling the paths in the tree, attractors with different directions can be generated. Several examples are given to illustrate these new directional attractors.