摘要
用标度变换法计算分形维数时,即使对理想的自相似结构,公式N(ε)=ε^(-D)也不是对所有的测量标度ε都成立,仅在ε取α~n的特征尺度时才严格成立。这里α为分形集的相似比,而当ε→0时,该式可近似成立。分析有限嵌套自相似结构模型得到一系列重要的结论。双对数回归直线计算分维在理论上是不正确的,可用修正公式直接计算,但问题仍未解决。看来标度变换法能否有效地解决简单分形维数的计算,还要进一步研究。
When calculating fractal dimension by scale transformation we found that the definition A(ε) = ε-D is not suitable for all of the measuring scale ε, and only when e showing a, characteristic scale that is it tenable rigidly. Here we definite a similarity ratio of fractals set, and this formulas be approximately tenable. A series of important conclusion was got after analyzing the model of finite embeded self-similiar structure. It is incorrect in theory to calculate fractal dimension through the way of log-log regression line, but by using directly the modifier formulas.
出处
《内陆地震》
1992年第3期217-222,共6页
Inland Earthquake
关键词
标度变换法
嵌套结构
分维
地震
Scale transformation Simple fractal dimension Self-similiar structure
