Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Fractal Valued Random Iteration Algorithm and Fractal Hierarchy   We describe new families of random fractals, referred to as "V-variable",
which are intermediate between the notions of deterministic and of standard
random fractals. The parameter V describes the degree of "variability" : at
each magnification level any V-variable fractals has at most V key "forms" or
"shapes". V-variable random fractals have the surprising property that they can
be computed using a forward process. More precisely, a version of the usual
Random Iteration Algorithm, operating on sets (or measures) rather than points,
can be used to sample each family. To present this theory, we review relevant
results on fractals (and fractal measures), both deterministic and random. Then
our new results are obtained by constructing an iterated function system (a
super IFS) from a collection of standard IFSs together with a corresponding set
of probabilities. The attractor of the super IFS is called a superfractal; it
is a collection of V-variable random fractals (sets or measures) together with
an associated probability distribution on this collection. When the underlying
space is for example $\mathbb{R}^{2}$, and the transformations are
computationally straightforward (such as affine transformations), the
superfractal can be sampled by means of the algorithm, which is highly
efficient in terms of memory usage. The algorithm is illustrated by some
computed examples. Some variants, special cases, generalizations of the
framework, and potential applications are mentioned.

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The categories of this paper are: supr-con
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The categories of this paper are: eess
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga