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Unformatted text preview: ijn sequences
≈ 1.31 × 10350 IFS forgeries of natural fractals If IFS just generated the gasket and its relatives, this approach would be of
interest to geometers (including me), but maybe not to many others. We remember that a large part of Mandelbrot’s motivation was to understand the 2.6. IFS FORGERIES OF NATURAL FRACTALS 67 roughness of objects in nature. His insight was that much of physical roughness could be explained by by using symmetry under magniﬁcation. Benoit’s
thinking never strayed far from Nature.
Mirroring this, Michael Barnsey interested many, many people in IFS by Fig.
3 of , a realistic image of a black spleenwort fern constructed using only four
transformations. This generated much interest, and at least indirectly prepared
the way for fractal landscape systhesis and many other visual eﬀects. In this
section we learn to make fractal forgeries of some simple natural iamges.
The left side of Fig. 2.33 shows a fractal tree, two branches left, two branches
right, each of these having tw banches on each side, and so on. This is straightforward except possibly for the trunk. The right side, a fractal fern, involves a
more subtle decomposition, so will be treated more extensively....
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