Using computer algebra methods to determine the chemical dimension of finitely ramified Sierpinski carpets
Astrid Franz, Christian Schulzky, Karl Heinz Hoffmann · ACM SIGSAM Bulletin · 2002
We present a new algorithm for calculating the chemical dimension d 1 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.