Journal of Statistical Physics

, Volume 58, Issue 5, pp 1109–1126

On the structure of Mandelbrot's percolation process and other random cantor sets

  • F. M. Dekking
  • R. W. J. Meester

DOI: 10.1007/BF01026566

Cite this article as:
Dekking, F.M. & Meester, R.W.J. J Stat Phys (1990) 58: 1109. doi:10.1007/BF01026566


We consider generalizations of Mandelbrot's percolation process. For the process which we call the random Sierpinski carpet, we show that it passes through several different phases as its parameter increases from zero to one. The final section treats the percolation phase.

Key words

Percolation processrandom fractal setrandom substitutionHausdorff dimension

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • F. M. Dekking
    • 1
  • R. W. J. Meester
    • 1
  1. 1.Delft University of TechnologyThe Netherlands