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
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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 -