Fractals *
*Note: This is an abbreviated Project Idea, without notes to start your background research, a specific list of materials, or a procedure for how to do the experiment. You can identify abbreviated Project Ideas by the asterisk at the end of the title. If you want a Project Idea with full instructions, please pick one without an asterisk.
Abstract
A fractal is, "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced/size copy of the whole" (Mandelbrot, 1982). There are many different fractal patterns, each with unique properties and typically named after the mathematician who discovered it. A fractal increases in complexity as it is generated through repeated sets of numbers called iterations. There are many interesting projects exploring fractal geometry that go beyond the project outlined in the Exploring Fractals Science Buddies project idea. For example, can you show that the perimeter of the Koch Fractal increases infinitely even though the area is finite? (Lanius, 2004) Can you use fractal geometry to investigate and model objects from nature? Try matching up a fractal pattern with the natural geometry of clouds, ferns, flowers, shells, or trees (Frame and Mandelbrot, date unknown). Can you program a java applet to draw different fractals? (Devaney, 1999)Share your story with Science Buddies!
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Last edit date: 2013-01-10
Bibliography
- Devaney, R.L., 1999. "Java Applets," Boston University, Dept. of Mathematics and Statistics. [accessed: 5/1/06] http://math.bu.edu/DYSYS/applets/index.html
- Frame, M. and Mandelbrot, B. B. Date unknown. "Fractal Geometry Panorama," Mathematics Department, Yale University. [accessed: 5/1/06] http://classes.yale.edu/Fractals/Panorama/
- Lanius, C., 2004. "The Koch Snowflake," Rice University, Department of Mathematics. [accessed: 5/1/06] http://math.rice.edu/~lanius/frac/koch.html
- Mandelbrot, B., 1982. The Fractal Geometry of Nature. New York, NY: W. H. Freeman & Co.
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