Stefano Maria Iacus and Davide La Torre
Fractals and Statistics: An R Package Called ifs
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Iterated Function Systems (IFSs) were born in mid eighties
(see Hutchinson, 1981 and Barnsley and Demko, 1985) as applications
of the theory of discrete dynamical systems and as useful tools to
build fractals and other similar sets. Some possible applications of
IFSs can be found in image processing theory (see e.g. the recent work
by Forte and Vrscay, 1994), in the theory of stochastic growth models
and in the theory of random dynamical systems. In particular they come
to great popularity when they have been proposed as the `definitive'
method of images compression. We do not discuss such aspect here but the
reader can refer, for example, to http://www.faqs.org/faqs/compression-faq/.

We propose to apply (affine) IFSs  to statistics. In particular, we are
concerned with the problem of distribution function estimation and related
quantities like the characteristic and density function.