Connectivity properties of Mandelbrot's percolation process


Journal Article

In 1974, Mandelbrot introduced a process in [0, 1]2 which he called "canonical curdling" and later used in this book(s) on fractals to generate self-similar random sets with Hausdorff dimension D∈(0,2). In this paper we will study the connectivity or "percolation" properties of these sets, proving all of the claims he made in Sect. 23 of the "Fractal Geometry of Nature" and a new one that he did not anticipate: There is a probability pc∈(0,1) so that if p

Full Text

Duke Authors

Cited Authors

  • Chayes, JT; Chayes, L; Durrett, R

Published Date

  • March 1, 1988

Published In

Volume / Issue

  • 77 / 3

Start / End Page

  • 307 - 324

Electronic International Standard Serial Number (EISSN)

  • 1432-2064

International Standard Serial Number (ISSN)

  • 0178-8051

Digital Object Identifier (DOI)

  • 10.1007/BF00319291

Citation Source

  • Scopus