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 fractal square F is essentially a planar self-similar set satisfying the set equation F=(F+D)/n with n≥2 and D?{0,1,...,n-1}~2.In this paper,we study the topological classification of fractal squares in the case of...A fractal square F is essentially a planar self-similar set satisfying the set equation F=(F+D)/n with n≥2 and D?{0,1,...,n-1}~2.In this paper,we study the topological classification of fractal squares in the case of n=4 and |D|=4.展开更多
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.
基金Supported by the Soft Science Research of Xiangyang City in 2019。
文摘A fractal square F is essentially a planar self-similar set satisfying the set equation F=(F+D)/n with n≥2 and D?{0,1,...,n-1}~2.In this paper,we study the topological classification of fractal squares in the case of n=4 and |D|=4.
