| The computation of the various dimensions of fractal sets is very important in fractal geometry research. To generate a fractal set, We have many methods, and the iterated function system is in common use. The generalized iterated function system and the graph-directed iterated function system are two general forms. Since the fractal set generated is the projection in the Euclidean space of the code space corresponding to the iterated function system, there's close relationship between the fractal set and the code space.In this paper, we will construct a suitable measure(equilibrium measure) in the code space and define one kind of dimension(equilibrium dimension) to describe the subsets of the code space. Then we will prove that the Hausdorff dimension of fractal set can be estimated or determined by the new dimension if some suitable separation conditions are satisfied. By that, we will estimate the dimension of a fractal set generated by a graph-directed iterated function system. |
