Trees with non-regular fractal boundary |
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| Authors: | Jing Hu Yu Yi Ming Ding |
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| Affiliation: | (1) Department of Mathematics, School of Sciences, Wuhan University of Technology, Wuhan, 430070, P. R. China;(2) Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, P. R. China |
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| Abstract: | For any given 0 < α < β < ∞, we construct a tree such that under tree metric, the Hausdorff dimension of the corresponding boundary is α, but both the Packing dimension and the boxing dimension are β. Applying the connection between tree and iterated functions system, nonregular fractal sets on real line are constructed. Moreover, the method adopted in our paper is different from those which have been used before for constructing non-regular fractal set in general metric space. This research is partially supported by the National Science Foundation of China |
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| Keywords: | tree boundary fractal dimensions non-regularity recursive structures |
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