NEGATIVE FRACTAL DIMENSIONS AND MULTIFRACTALS

被引:124
作者
MANDELBROT, BB [1 ]
机构
[1] YALE UNIV,DEPT MATH,NEW HAVEN,CT 06520
来源
PHYSICA A | 1990年 / 163卷 / 01期
关键词
D O I
10.1016/0378-4371(90)90339-T
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A new notion of fractal dimension is defined. When it is positive, it effectively falls back on known definitions. But its motivating virtue is that it can take negative values, which measure usefully the degree of emptiness of empty sets. The main use concerns random multifractals for which f(α) < 0 for some α's. The positive f(α) are show to define a "typical" distribution of the measure, while the negative f(α) rule the sampling variability. Negative dimensions are best investigated using "supersamples." Applications are to turbulence and to DLA. © 1990.
引用
收藏
页码:306 / 315
页数:10
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