Self-similarity and covered neighborhoods of fractals: A random walk test

D. Stauffer*, A. Aharony, B. B. Mandelbrot

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


A strong version of the property of self-similarity is described, and it is shown that this property is satisfied by random walks on a simple cubic lattice. When each site visited by the walk is surrounded by a small cube, the total volume of these covering cubes depends on the cube size, the size of the region investigated, and the length of the walk. We find that for long walks at a fixed ratio of cube to region size the filling ratio is roughly constant.

Original languageEnglish
Pages (from-to)1-5
Number of pages5
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1
StatePublished - 15 May 1993


FundersFunder number
German-Israeli Foundation for Scientific Research and Development
Bundesministerium für Forschung und Technologie0326657D


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