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Title

Using Computer Algebra Methods to Determine the Chemical Dimension of Finitely Ramified Sierpinski Carpets
Authors

Astrid Franz
Organization: Technische Universitat
Department: Institut fur Physik
Christian Schulzky
Organization: University of Western Ontario
Department: Applied Mathematics
Karl Heinz Hoffmann
Organization: Technische Universitat
Department: Institut fur Physik
Journal / Anthology

ACM SIGSAM Bulletin
Year: 2002
Volume: 36
Issue: 2
Page range: 18-30
Description

We present a new algorithm for calculating the chemical dimension dl of finitely ramified Sierpinski carpets. Using an algorithm of Dijkstra, we compute iteratively, using Mathematica, the shortest paths through a carpet. The scaling exponent of the lengths of these shortest paths over the linear size of the carpet is d(min) the minimum path dimension, which is related to the chemical dimension.
Subjects

*Mathematics > Discrete Mathematics > Cellular Automata
*Science > Chemistry