| 经典分形集测度上估的计算机搜索Ⅱ──对典型例子Sierpinski垫片计数技术和格点跟踪技术的剖析 |
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| 引用本文： | 王何宇,王兴华.经典分形集测度上估的计算机搜索Ⅱ──对典型例子Sierpinski垫片计数技术和格点跟踪技术的剖析[J].计算数学,1999,21(3):345-354. |
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| 作者姓名： | 王何宇 王兴华 |
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| 作者单位： | 1. 杭州大学计算机基础教学部
2. 杭州大学数学与信息科学系 |
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| 基金项目： | 国家攀登计划，浙江省自然科学基金，，，， |
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| 摘 要： | A upper estimate function ν(x) of Hausdorff measure Hs (S) ofSierpinski Gasket is given. A mathematical representation of the upperapproximate value νN (x) to ν(x) and a simple algorithm ofνN (x) based on lattice tracing technique are also derived. As asimple corollary, the estimation Hs(S)≤ min ν15 (n·10-5)=ν15 (0.50783)=0.81794 …is obtained.
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| 关 键 词： | Hausdorff 测度 计算机搜索 计数技术 格点跟踪技术 Sierpinski垫片 |
| 修稿时间： | 1998年4月26日. |
COMPUTER SEARCH FOR THE UPPER ESTIMATION OF HAUSDORFF MEASURE OFCLASSICAL FRACTAL SETS II--ANALYSIS OF COUNTING TECHNIQUE ANDLATTICE TRACING TECHNIQUE FOR THE TYPICAL EXAMPLE OF SIERPINSKI GASKET |
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| Wang Heyu,Wang Xinghua.COMPUTER SEARCH FOR THE UPPER ESTIMATION OF HAUSDORFF MEASURE OFCLASSICAL FRACTAL SETS II--ANALYSIS OF COUNTING TECHNIQUE ANDLATTICE TRACING TECHNIQUE FOR THE TYPICAL EXAMPLE OF SIERPINSKI GASKET[J].Mathematica Numerica Sinica,1999,21(3):345-354. |
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| Authors: | Wang Heyu Wang Xinghua |
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| Institution: | Wang Heyu; Wang Xinghua(Hangzhou University, Hangzhou) |
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| Abstract: | A upper estimate function v(x) of Hausdorff measure H'(S) of Sierpinski Gas-ket is given. A mathematical representation of the upper approximate value uN(x)to u(x) and a simple algorithm of uN(x) based on lattice tracing technique are also derived. As a simple corollary, the estimation H'(S) min u15(n 10-5)=u15(0.50783)=0.81794'is obtained. |
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| Keywords: | Hausdorff measure Computer search Counting technique Lattice tracing technique Sierpinski gasket |
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