Unformatted text preview: generated by this IFS. Here the pieces
have been pulled apart to more clearly reveal their individual natures. Figure 2.34: Left: fractal tree with halftrunk. Right: fractal tree with its main
pieces pulled apart.
The fern is a bit more diﬃcult. A ﬁrst guess at decomposing the fern might
be discouraging: the bottom left and right fronds are small copies of the fern, as
are the fronds left and right above those, as are the fronds left and right above
those, and so on. Viewed this way, the fern is made of dozens, maybe hundreds
(in fact, inﬁnitely many, if we think of the image as a pixelated version of a
mathematical fractal) of smaller copies of itself. Sometimes, the most obvious 2.6. IFS FORGERIES OF NATURAL FRACTALS 69 way to decompose a fractal does not lead to an IFS with the smallest number
of rules.
A simpler shape, a relative of the gasket, will guide us in decomposing the
fern. The left side of Fig. 2.35 can be decomposed into a row of four smaller
copies along the bottom, a row of four slightly smalle...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.
 Fall '14
 AmandaFolsom
 Geometry, Fractal Geometry, Limits, The Land

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