Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the...Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.展开更多
In this paper, we study the connectedness of the invariant sets of a graph-directed iterated function system（IFS）. For a graph-directed IFS with N states, we construct N graphs. We prove that all the invariant sets ...In this paper, we study the connectedness of the invariant sets of a graph-directed iterated function system（IFS）. For a graph-directed IFS with N states, we construct N graphs. We prove that all the invariant sets are connected, if and only if all the N graphs are connected; in this case, the invariant sets are all locally connected and path connected. Our result extends the results on the connectedness of the self-similar sets.展开更多
A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..
This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D = (r1D) ∪ (r2D + (1 + r1 - r2 - r3)/2) ∪ (r3D + 1 - r3) and E = (r1E) ∪ (r2E + 1 - r2 -r3) ∪ (r3E + 1 - r3),and ...This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D = (r1D) ∪ (r2D + (1 + r1 - r2 - r3)/2) ∪ (r3D + 1 - r3) and E = (r1E) ∪ (r2E + 1 - r2 -r3) ∪ (r3E + 1 - r3),and proves that D and E areLipschitz equivalent if and only if there are positive integers m and n such that rm1= rn3.展开更多
文摘Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.
基金Supported by the Teaching Research Project of Hubei Province(2013469)the 12th Five-Year Project of Education Plan of Hubei Province(2014B379)
文摘In this paper, we study the connectedness of the invariant sets of a graph-directed iterated function system（IFS）. For a graph-directed IFS with N states, we construct N graphs. We prove that all the invariant sets are connected, if and only if all the N graphs are connected; in this case, the invariant sets are all locally connected and path connected. Our result extends the results on the connectedness of the self-similar sets.
文摘A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10301029,10671180,10601049) and Morningside Center of Mathematics
文摘This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D = (r1D) ∪ (r2D + (1 + r1 - r2 - r3)/2) ∪ (r3D + 1 - r3) and E = (r1E) ∪ (r2E + 1 - r2 -r3) ∪ (r3E + 1 - r3),and proves that D and E areLipschitz equivalent if and only if there are positive integers m and n such that rm1= rn3.
