MULTIFRACTALITY OF THE HARMONIC MEASURE ON FRACTAL AGGREGATES, AND EXTENDED SELF-SIMILARITY

被引:25
作者
MANDELBROT, BB
EVERTSZ, CJG
机构
[1] YALE UNIV,DEPT MATH,NEW HAVEN,CT 06520
[2] YALE UNIV,DEPT APPL PHYS,NEW HAVEN,CT 06520
来源
PHYSICA A | 1991年 / 177卷 / 1-3期
关键词
D O I
10.1016/0378-4371(91)90177-E
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We show that DLA follows a surprising new scaling rule. It expresses that the screened region, in which the harmonic measure is tiny, increases more than proportionately as the cluster grows. This scaling rule also gives indirect evidence that the harmonic measure of lattice DLA follows a hyperbolic probability distribution of exponent equal to 1. This distribution predicts that sample moments behave erratically, hence explains why the common restricted multifractal formalism fails to apply to DLA.
引用
收藏
页码:386 / 393
页数:8
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