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Unformatted text preview: you will change the rules to address those problems. Repeat until you
are satisﬁed with the picture.
(a) a leaf, (b) a cloud, (c) a mountain range, (d) broccoli, (e) a starﬁsh, and (f)
a caricature of a face. (A surprisingly eﬀective example of this was done by a
student in 1993.) 2.7 Finding aﬃne transformations from point
images In the last section we saw how to estimate the parameters for IFS that generate
forgeries of natural objects. While some simple relatives of the gasket, especially
those involving both reﬂections and rotations, can be a bit challenging, still
they are relatively clean. Natural fractal IFS can involve aﬃnities (r = s) or 78 CHAPTER 2. ITERATED FUNCTION SYSTEMS distortions (θ = ϕ), not so easy to parse visually. So in this section we develop
a more mechanical, procedure. Here we need only locate the images of selected
points, not try to identify transformed copies of the whole shape. Speciﬁcally,
take three easily identiﬁed, non-collinear points in...
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