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Laser Teaching Center, Physics and Astronomy Fractals are geometric curves or shapes that are infinitely complex. When divided into parts, each piece is a reduced copy of the whole, a feature called self-similarity. Fractals can be described by equations with non-integer dimensions, known as fractal dimensions. Fractal forms are common in nature. Some examples are snowflakes, clouds, crystals, mountain ranges and coastlines, lightning flashes, and systems of roots or blood vessels. Fractal patterns are also often seen as artworks or colorful computer displays. A simple example is the snowflake or Koch curve, which is generated by replacing a line segment with four lines, each one-third the length of the original. When this process is iterated the resulting chain of line segments becomes infinitely long. In 1999, David Sweet, Edward Ott and James A. Yorke analyzed the multiple reflections that occur between the surfaces of four reflective spheres when these are stacked up in a tetrahedral arrangement [``Topology in chaotic scattering,'' Nature 399, 315 (May 27, 1999)]. The goal of my project is to build a full size copy of the sphere arrangement discussed in this paper and to understand the fractal patterns produced by the multiple reflections.
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