240 figure 239 two fractal snowakes elton 48 gave a

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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 right-most s...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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