FRACTALS Radmaste分形RADMSTE.docVIP

FRACTALS CAN BE FUN! AMESA workshop by Ingrid Sapire, 28 May 2005 Fractal geometry and chaos theory provide us with a new perspective to view the world. For centuries the straight line was used as a basic building block to understand the objects around us. Chaos science uses a different geometry called fractal geometry. Fractal geometry is a new language used to describe, model and analyze complex forms found in nature. These forms grow by repeated similar breakdowns. The study of fractals has been made possible by the development of computer technology. This explains why these forms, which have existed in nature over all time, have only begun to be deciphered by mathematicians over the past 40 years. DEFINITION:A fractal is a geometric shape that it self-similar and has fractional (fractal) divisions. This fractional division can be used to investigate patterns which develop if you follow the sequence of shapes formed by a fractal division. If you are interested in studying the numeric patterns we can find using fractals, DISCOVERING ALGEBRA, An Investigative Approach, Murdock et al, (2002) is an excellent reference you could use. When you look at a mountain from far away, it looks jagged and irregular. When drive closer to the mountain, it still looks jagged and irregular. When you go walking up the mountain, it still looks jagged and irregular. The closer you get to the mountain, you see the same pattern, in patterns that emerge, as you look closer and closer. These patterns share a close up vs panoramic symmetry, rather than a right vs left symmetry that we see in mirror images. The illustrations on the next page explain this idea. Fractal “symmetry” : close up vs panoramic Reflection (line) symmetry : right vs left A few things that fractals can model are: Geologic activity such as the development of a coastline /raeh/fractalContinentColor.jpg Human body patterns such as the circulatory system Growth of plants Ice formation of snow flakes You can dra