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Areas of Science
Time Required
Long (2-4 weeks)
*Note: For this science project you will need to develop your own experimental procedure. Use the information in the summary tab as a starting place. If you would like to discuss your ideas or need help troubleshooting, use the Ask An Expert forum. Our Experts won't do the work for you, but they will make suggestions and offer guidance if you come to them with specific questions.

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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)


  • Devaney, R.L., 1999. Java Applets, Boston University, Dept. of Mathematics and Statistics. Retrieved 5/1/06.
  • Frame, M. and Mandelbrot, B. B. Date unknown. Fractal Geometry Panorama, Mathematics Department, Yale University. Retrieved 5/1/06.
  • Lanius, C., 2004. The Koch Snowflake, Rice University, Department of Mathematics. Retrieved 5/1/06.
  • Mandelbrot, B., 1982. The Fractal Geometry of Nature. New York, NY: W. H. Freeman & Co.
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Mathematicians are part of an ancient tradition of searching for patterns, conjecturing, and figuring out truths based on rigorous deduction. Some mathematicians focus on purely theoretical problems, with no obvious or immediate applications, except to advance our understanding of mathematics, while others focus on applied mathematics, where they try to solve problems in economics, business, science, physics, or engineering. Read more
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Are you interested in developing cool video game software for computers? Would you like to learn how to make software run faster and more reliably on different kinds of computers and operating systems? Do you like to apply your computer science skills to solve problems? If so, then you might be interested in the career of a computer software engineer. Read more

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MLA Style

Science Buddies Staff. "Fractals." Science Buddies, 20 Nov. 2020, https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p031/pure-mathematics/fractals. Accessed 7 June 2023.

APA Style

Science Buddies Staff. (2020, November 20). Fractals. Retrieved from https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p031/pure-mathematics/fractals

Last edit date: 2020-11-20
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