FractionalGeometry-Chap2

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Unformatted text preview: ivalent of videofeedback with mirrors. Right: an example of a fractal generated with this arrangement. On the left of Fig. 2.50 we see the negative of the fractal image of Fig. 2.49, together with three initial points A0 , B0 , and C0 . On the right we see four sets of image points, the images of the initial points, one set for each main piece of the image. The image points A1 , B1 , and C1 are placed in the upper piece by identifying points corresponding to the initial points. The bottom piece is produced by two reflections, equivalently, by a rotation. Take the initial point A0 to be the origin and measure the coordinates of B0 and C0 , obtaining (3.6, 9.5) and (14.3, 6.7). Measure the coordinates of the image points, obtaining these values. 84 CHAPTER 2. ITERATED FUNCTION SYSTEMS Figure 2.50: Left: The negative of a two mirror videofeedback image with initial points indicated. Right: The four sets of image points. A1 B1 C1 A2 B2 C2 (6.0, 3.9) (3.4, 7.4) (7.5, 11.0) (5.7, 3.5) (1.1, 3.9) (0, 0) A3 B3 C3 A4 B4 C4 (8.2, 2....
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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