Patterns pervade the natural world as well as the world of the intellect. In the biological realm, we are quite aware that when we mentally visualize a zebra we probably first think of its most prominent feature, its stripes. When we look at certain butterflies, it is usually the colorful markings on the wings that grab our attention. If we study magnified ice crystals, our interest is captivated by the richness and regularity of the patterns displayed. If we go into a wallpaper store to shop for our home, we can be overwhelmed by the artistic choices available. If we listen to a piece by Beethoven we are struck by the musical tapestry that one of the world’s greatest composers has woven. If we talk to a scientist we will soon find that his or her goal in life is usually to discover (impose?) some underlying pattern to the phenomena under investigation. Clearly, patterns are important in many different ways. As a consequence, the scientific study of pattern formation is a very large field, and any attempt to systematically cover the topic is far beyond the aim or scope of this text.
KeywordsFractal Dimension Fractal Pattern Sierpinski Gasket Capacity Dimension Ring Particle
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