2008
DOI: 10.1016/j.physa.2008.05.034
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A generalization of the inhomogeneity measure for point distributions to the case of finite size objects

Abstract: The statistical measure of spatial inhomogeneity for n points placed in χ cells each of size k×k is generalized to incorporate finite size objects like black pixels for binary patterns of size L×L. As a function of length scale k, the measure is modified in such a way that it relates to the smallest realizable value for each considered scale. To overcome the limitation of pattern partitions to scales with k being integer divisors of L we use a sliding cell-sampling approach. For given patterns, particularly in… Show more

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Cited by 5 publications
(21 citation statements)
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“…For the sake of clarity a window of width k we identify with the one-dimensional cell of length k while for patterns the cell is of size k × k. In the following we shall simply use the notion "cell" that size be clear from the system's dimension d = 1, 2. To overcome the limitation of standard pattern partitions (into non-overlapping cells) to the scales, for which k is an integer divisor of L here we use a sliding cell-sampling (SCS) approach [7]. To control cell statistics a simple condition for this method is also further given in section 2.4.…”
Section: Actual and Reference Macrostatesmentioning
confidence: 99%
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“…For the sake of clarity a window of width k we identify with the one-dimensional cell of length k while for patterns the cell is of size k × k. In the following we shall simply use the notion "cell" that size be clear from the system's dimension d = 1, 2. To overcome the limitation of standard pattern partitions (into non-overlapping cells) to the scales, for which k is an integer divisor of L here we use a sliding cell-sampling (SCS) approach [7]. To control cell statistics a simple condition for this method is also further given in section 2.4.…”
Section: Actual and Reference Macrostatesmentioning
confidence: 99%
“…1(b) in Ref. [7,13]. Instead of preferred here Greek letter κ, the notation χ a has been used in Ref.…”
Section: Actual and Reference Macrostatesmentioning
confidence: 99%
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“…An overview of an aspect of work in that area is given in [16]. For example, Zwicky [17] uses an approach similar to (2).…”
Section: Related Workmentioning
confidence: 99%