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Our algorithm is, in
fact, a version of a nonlinear iterated function system
(IFS).
Figure:
The classical fractal: Sierpinski Triangle generated by an Iterated Function System.

Such algorithms are known to produce complex geometrical
structures by repeated application of several noncommuting affine
maps. The best known example is the Sierpinski triangle
generated by random application of matrices to the vector:

(21) 
where is given by

(22) 
and
(Our matrices encode affine transformations 
usually separated into a matrix and a translation
vector.) At each step one of the three transformations is selected with probability . After each
transformation the transformed vector is plotted on the
plane. Theoretical papers on IFSs usually assume that the system
is hyperbolic that is that each transformation is a
contraction, i.e. the distances between points get smaller and
smaller. It was shown in [17] that this assumption can
be essentially relaxed when transformations are nonlinear and act
on a compact space  as is in the case of quantum fractals we are
dealing with.
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