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Dynamical partitions of space in any dimension

Aste, T; (1998) Dynamical partitions of space in any dimension. Journal of Physics A: Mathematical and General , 31 (43) 8577 - 8593. 10.1088/0305-4470/31/43/003.

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Abstract

Topologically stable cellular partitions of D-dimensional spaces are studied. A complete statistical description of the average structural properties of such partitions is given in terms of a sequence of D/2 - 1 (or D-1/2) variables for D even (or odd). These variables are the average coordination numbers of the 2k-dimensional polytopes (2k < D) which make up the cellular structure. A procedure to produce D-dimensional space partitions through cell-division and cell-coalescence transformations is presented. Classes of structures which are invariant under these transformations are found and the average properties of such structures are illustrated. Homogeneous partitions are constructed and compared with the known structures obtained by Voronoï partitions and sphere packings in high dimensions.

Type:Article
Title:Dynamical partitions of space in any dimension
DOI:10.1088/0305-4470/31/43/003
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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