An Introduction to Fractals By Brian Feuer What

An Introduction to Fractals By: Brian Feuer

What is a Fractal? A word coined by Benoit Mandelbrot in 1975 to describe shapes that are “selfsimilar” and are generated by a repeating pattern, typically a “recursive” or “iterative” process. Fractals are independent of scale.

Components of a Fractal Ø Self • • Similarity Two or more objects having the same characteristics. In fractals, the shapes of lines at different iterations look like smaller versions of the earlier shapes. Otherwise put, the shapes look the same at different magnifications. Ø Iteration • • Repeating a set or rules or steps over and over. One single step is called an iterate. Ø Recursion. Given some starting information and a rule for how to use it to get new information, the rule is then repeated using the new information.

Fractals in Nature Can you think of any fractals found in nature?

More Fractals in Nature

Complex Fractals

References n n http: //www. dcet. k 12. de. us/teach/quest/shari. htm by Shari Galgano http: //math. rice. edu/~lanius/frac/ by Cynthia Lanius http: //astronomy. swin. edu. au/~pbourke/fractals/fuzzylogic/ by Roger Bagula http: //occawlonline. pearsoned. com/bookbind/pubbooks/bills tein_awl/medialib/shodor_site/lessons/frac 1. html by The Shodor Education Foundation, Inc.