FractionalGeometry-Chap2

Together and range over the product of two circles

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Unformatted text preview: arrangement of two mirrors and monitor for this experiment. A video camera is pointed at the monitor and mirrors, and the signal from the camera fed into the monitor. With appropriate adjustment of camera zoom, stable fractal images can be produced. An example is seen on the right side of Fig. 2.49. In the middle of Fig. 2.49 we show how to unpack the basic structure of the two mirror videofeedback, and ﬁnd the main aspects of the equivalent IFS. The image of the monitor in the left mirror is obtained by reﬂecting across the y -axis; the image of the monitor in the bottom mirror is obtained by reﬂecting across the x-axis. Both mirrors include reﬂections of a portion of the image in the other mirror. Both compositions of reﬂections across the x- and y -axes are equivalent to rotation about the origin by π . These ideas will guide our selection of target and image points. image reflect across y rotate reflect across x rotate Figure 2.49: Left: four images from a monitor and two mirrors. Middle: IFS equ...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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