Multifractal lattice and group theory
The multifractal lattice Qmf is an object defined on a square using a section parameter ζ. Qmf has been used to study percolation in heterogeneous multifractal structures. In this work we use a group theory approach to explore mathematical properties of Qmf. The self-affine object Qmf is described by the combination of distinct discrete groups: the finite groups of rotation and inversion and the infinite groups of translation and dilation. We address the cell elements of the lattice Qmf using a Cayley tree. We determine the Cartesian coordinates of each cell using group properties in a recursive equation. The rich group structure of Qmf allows an infinite number of distinct tilling for a single ζ.
Year of publication: |
2005
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Authors: | Corso, G. ; Lucena, L.S. |
Published in: |
Physica A: Statistical Mechanics and its Applications. - Elsevier, ISSN 0378-4371. - Vol. 357.2005, 1, p. 64-70
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Publisher: |
Elsevier |
Saved in:
Online Resource
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