Unformatted text preview: the bottom of the stem of the fern is missing, so is the bottom of
the stem of each frond, the part of the frond that attaches it to the body of
the fern. These missing stem pieces continue to the fronds of the fronds, the
fronds of the fronds of the fronds, and so on forever. So we add a fourth rule
to make the bottom of the stem. The right side of Fig. 2.36 shows the fern
disassembled into these four pieces. The table below gives the complete ferm
IFS, with probabilities.
r
0.30
0.30
0.85
0 s
0.34
0.37
0.85
0.16 θ
ϕ
e
f
49◦
49◦
0
1.60
◦
◦
50
50
0
0.44
2.5◦
2.5◦
0
1.60
0
0
0
0
IFS for the fern of Fig. 2.33. prob
0.12
0.12
0.75
0.01 71 2.6. IFS FORGERIES OF NATURAL FRACTALS Fractal spirals are another family of visually interesting examples. The top
left of Fig. 2.37 shows a fractal spiral. While we might at ﬁrst see this as
made up of many smaller copies of the entire spiral, experience with the fern
suggests we decompose the spiral into two pieces: the rightmost s...
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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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