Fractal percolation and branching cellular automata

被引：3
|
作者：
Dekking, FM
von der Wal, P
机构：
[1] Thomas Stieltjes Inst Math, NL-2628 CD Delft, Netherlands
[2] Delft Univ Technol, NL-2628 CD Delft, Netherlands
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2001年 / 120卷 / 02期
关键词：
random fractal set; fractal percolation; multi-type branching;
D O I：
10.1007/PL00008784
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：
Branching cellular automata (BCA) are introduced as generalisations of fractal percolation by admitting neighbour dependence. We associate sequences of random sets with BCA's and study their convergence. In case of convergence we derive the Hausdorff dimension of the limit set and of its boundary. To accomplish the latter we proof that the boundary of a set generated by a BCA is again a set generated by a BCA.
引用
收藏
页码：277 / 308
页数：32
相关论文
共 50 条
  • [41] Characteristics of fractal cellular automata constructed from linear rules
    Yoshihiko Kayama
    Artificial Life and Robotics, 2020, 25 : 8 - 16
  • [42] A fractal model of granitic intrusion and variability based on cellular automata
    Xiong, Yihui
    Zuo, Renguang
    Clarke, Keith C.
    COMPUTERS & GEOSCIENCES, 2019, 129 : 40 - 48
  • [43] FRACTAL DIMENSION AT THE PHASE-TRANSITION OF INHOMOGENEOUS CELLULAR AUTOMATA
    DASILVA, LR
    JOURNAL OF STATISTICAL PHYSICS, 1988, 53 (3-4) : 985 - 990
  • [44] Study on Acoustic Field with Fractal Boundary Using Cellular Automata
    Komatsuzaki, Toshihiko
    Iwata, Yoshio
    CELLULAR AUTOMATA, PROCEEDINGS, 2008, 5191 : 282 - 290
  • [45] Characteristics of fractal cellular automata constructed from linear rules
    Kayama, Yoshihiko
    ARTIFICIAL LIFE AND ROBOTICS, 2020, 25 (01) : 8 - 16
  • [46] Stability of Cellular Automata Trajectories Revisited: Branching Walks and Lyapunov Profiles
    Jan M. Baetens
    Janko Gravner
    Journal of Nonlinear Science, 2016, 26 : 1329 - 1367
  • [47] Stability of Cellular Automata Trajectories Revisited: Branching Walks and Lyapunov Profiles
    Baetens, Jan M.
    Gravner, Janko
    JOURNAL OF NONLINEAR SCIENCE, 2016, 26 (05) : 1329 - 1367
  • [48] CELLULAR-AUTOMATA APPROACH TO SITE PERCOLATION ON Z(2) - A NUMERICAL STUDY
    BLANCHARD, P
    GANDOLFO, D
    JOURNAL OF STATISTICAL PHYSICS, 1993, 73 (1-2) : 399 - 408
  • [49] Cellular automata with rare events; Resolution of an outstanding problem in the bootstrap percolation model
    De Gregorio, P
    Lawlor, A
    Bradley, P
    Dawson, KA
    CELLULAR AUTOMATA, PROCEEDINGS, 2004, 3305 : 365 - 374
  • [50] MODELING FRACTAL CRYSTALS FORMING ON THE SURFACE OF STAINLESS STEEL BY CELLULAR AUTOMATA
    Burtsev, A. A.
    Butkovskii, O. Ya
    PHYSICAL AND CHEMICAL ASPECTS OF THE STUDY OF CLUSTERS NANOSTRUCTURES AND NANOMATERIALS, 2018, (10) : 187 - 195
12345