TY - JOUR

T1 - Self-similarity and covered neighborhoods of fractals

T2 - A random walk test

AU - Stauffer, D.

AU - Aharony, A.

AU - Mandelbrot, B. B.

N1 - Funding Information:
We thank the German-Israeli foundation and BMFT grant 0326657D for partial support of this work, GMD St. Augustin and KFA Jiilich for use of their parallel i860 computers, and J. J/ickle for discussions.

PY - 1993/5/15

Y1 - 1993/5/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34547241180&partnerID=8YFLogxK

U2 - 10.1016/0378-4371(93)90076-G

DO - 10.1016/0378-4371(93)90076-G

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:34547241180

SN - 0378-4371

VL - 196

SP - 1

EP - 5

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1

ER -