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Using Computer Algebra Methods to Determine the Chemical Dimension of Finitely Ramified Sierpinski Carpets
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| Organization: | Technische Universitat |
| Department: | Institut fur Physik |
| Organization: | University of Western Ontario |
| Department: | Applied Mathematics |
| Organization: | Technische Universitat |
| Department: | Institut fur Physik |
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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.
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