多重分形盒计数算法中的划分方案和不可分盒尺寸
Partitioning Schemes and Non-Integer Box Sizes for the Box-Counting Algorithm in Multifractal Analysis
摘要：
通过计算奇异谱和盒概率分布，比较了多重分形分析中盒计数算法的不同划分方案。作为模型系统，我们使用安德森模型的本地化在二维和三维。我们表明，分区方案，其中包括无限制的值的框大小和平均在所有框的起源导致较小的误差界比标准方法使用的线性系统的大小和框大小的整数比，发现由罗德里格斯等人（Eur. B 67，77-82（2009））以产生最可靠的结果。
英文摘要：
We compare different partitioning schemes for the box-counting algorithm in the multifractal analysis by computing the singularity spectrum and the distribution of the box probabilities. As model system we use the Anderson model of localization in two and three dimensions. We show that a partitioning scheme which includes unrestricted values of the box size and an average over all box origins leads to smaller error bounds than the standard method using only integer ratios of the linear system size and the box size which was found by Rodriguez et al. (Eur. Phys. J. B 67, 77-82 (2009)) to yield the most reliable results.
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