Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anisotropic covering of fractal sets   We consider the optimal covering of fractal sets in a two-dimensional space
using ellipses which become increasingly anisotropic as their size is reduced.
If the semi-minor axis is \epsilon and the semi-major axis is \delta, we set
\delta=\epsilon^\alpha, where 0<\alpha<1 is an exponent characterising the
anisotropy of the covers. For point set fractals, in most cases we find that
the number of points N which can be covered by an ellipse centred on any given
point has expectation value < N > ~ \epsilon^\beta, where \beta is a
generalised dimension. We investigate the function \beta(\alpha) numerically
for various sets, showing that it may be different for sets which have the same
fractal dimension.

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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org