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# Fractals *

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 Areas of Science Pure Mathematics Difficulty 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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## 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)

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### MLA Style

Science Buddies Staff. "Fractals." Science Buddies, 28 July 2017, https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p031/pure-mathematics/fractals?class=AQUiGtc-1Bh38MDlo97wL_1ghno3IPhJr8wR7_1n2po7C6DANsw5WlwSVMNAna3uvuRZhBso-30J_DRPR3H0Oqsa. Accessed 6 Apr. 2020.

### APA Style

Last edit date: 2017-07-28

## Experimental Procedure

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.

If you want a Project Idea with full instructions, please pick one without an asterisk (*) at the end of the title.

## Share your story with Science Buddies!

The Ask an Expert Forum is intended to be a place where students can go to find answers to science questions that they have been unable to find using other resources. If you have specific questions about your science fair project or science fair, our team of volunteer scientists can help. Our Experts won't do the work for you, but they will make suggestions, offer guidance, and help you troubleshoot.

## If you like this project, you might enjoy exploring these related careers:

### Mathematician

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### Computer Programmer

Computers are essential tools in the modern world, handling everything from traffic control, car welding, movie animation, shipping, aircraft design, and social networking to book publishing, business management, music mixing, health care, agriculture, and online shopping. Computer programmers are the people who write the instructions that tell computers what to do. Read more

### Math Teacher

Math teachers love mathematics and understand it well, but much more than that, they enjoy sharing their enthusiasm for the language of numbers with students. They use a variety of tools and techniques to help students grasp abstract concepts and show them that math describes the world around them. By helping students conquer fears and anxieties about math, teachers can open up many science and technology career possibilities for students. Teachers make a difference that lasts a lifetime! Read more

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