Gudrun Schliecker 2001 J. Phys. A: Math. Gen. 34 25 doi:10.1088/0305-4470/34/1/302
Gudrun Schliecker
Show affiliationsThe correlations between topological and metric properties of fractal tessellations are analysed. To this end, Sierpinski cellular structures are constructed for different geometries related to Sierpinski gaskets and to the Apollonian packing of discs. For these geometries, the properties of the distribution of the cells' areas and topologies can be derived analytically. In all cases, an algebraic increase of the cell's average area with its number of neighbours is obtained. This property, unknown from natural cellular structures, confirms previous observations in numerical studies of Voronoi tessellations generated by fractal point sets. In addition, a simple rigorous scaling resp. multiscaling properties relating the shapes and the sizes of the cells are found.
28A80 Fractals (See also 37Fxx)
Issue 1 (12 January 2001)
Received 23 February 2000, in final form 20 October 2000
Gudrun Schliecker 2001 J. Phys. A: Math. Gen. 34 25
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