A lower bound on the box-counting dimension of crossings in fractal percolation

被引：9
|
作者：
Orzechowski, ME [1 ]
机构：
[1] Univ St Andrews, Inst Math, St Andrews KY16 9SS, Fife, Scotland
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1998年 / 74卷 / 01期
基金：
英国工程与自然科学研究理事会;
关键词：
fractal percolation; Mandelbrot percolation; box-counting dimension; Holder exponent;
D O I：
10.1016/S0304-4149(97)00117-8
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We consider Mandelbrot's fractal percolation process, obtained by repeated subdivision of the unit square, and obtain an explicit almost sure lower bound on the lower box-counting dimension of paths within the retained set that cross the square from left to right. (C) 1998 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：53 / 65
页数：13
相关论文
共 50 条
  • [1] ON THE PERFORMANCE OF BOX-COUNTING ESTIMATORS OF FRACTAL DIMENSION
    HALL, P
    WOOD, A
    [J]. BIOMETRIKA, 1993, 80 (01) : 246 - 252
  • [2] Enhancement of the Box-Counting Algorithm for fractal dimension estimation
    So, Gun-Baek
    So, Hye-Rim
    Jin, Gang-Gyoo
    [J]. PATTERN RECOGNITION LETTERS, 2017, 98 : 53 - 58
  • [3] Advances in the implementation of the box-counting method of fractal dimension estimation
    Foroutan-pour, K
    Dutilleul, P
    Smith, DL
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 1999, 105 (2-3) : 195 - 210
  • [4] Faster Estimation of the Correlation Fractal Dimension Using Box-counting
    Attikos, Christos
    Doumpos, Michael
    [J]. PROCEEDINGS OF THE 2009 FOURTH BALKAN CONFERENCE IN INFORMATICS, 2009, : 93 - +
  • [5] An improved box-counting method for image fractal dimension estimation
    Li, Jian
    Du, Qian
    Sun, Caixin
    [J]. PATTERN RECOGNITION, 2009, 42 (11) : 2460 - 2469
  • [6] A New Box-Counting Method for Image Fractal Dimension Estimation
    Xue, Song
    Jiang, Xinsheng
    Duan, Jimiao
    [J]. PROCEEDINGS OF 2017 3RD IEEE INTERNATIONAL CONFERENCE ON COMPUTER AND COMMUNICATIONS (ICCC), 2017, : 1786 - 1791
  • [7] AN IMPROVED BOX-COUNTING METHOD TO ESTIMATE FRACTAL DIMENSION OF IMAGES
    Yan, Jundong
    Sun, Yuanyuan
    Cai, Shanshan
    Hu, Xiaopeng
    [J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2016, 6 (04): : 1114 - 1125
  • [8] A new box-counting method for estimation of image fractal dimension
    Li, Jian
    Sun, Caixin
    Du, Qian
    [J]. 2006 IEEE INTERNATIONAL CONFERENCE ON IMAGE PROCESSING, ICIP 2006, PROCEEDINGS, 2006, : 3029 - +
  • [9] Measurements of fractal dimension by box-counting: a critical analysis of data scatter
    Buczkowski, S
    Hildgen, P
    Cartilier, L
    [J]. PHYSICA A, 1998, 252 (1-2): : 23 - 34
  • [10] Relationship between box-counting fractal dimension and properties of fracture networks
    Dong, Shaoqun
    Yu, Xiaohong
    Zeng, Lianbo
    Ye, Jing
    Wang, Leting
    Ji, Chunqiu
    Fu, Kaifeng
    Wang, Ruyi
    [J]. UNCONVENTIONAL RESOURCES, 2024, 4
12345