2. An Introduction to Fractals By: Brian Feuer

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

4. Components of a Fractal  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. 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. Otherwise put, the shapes look the same at different magnifications.  Iteration Repeating a set or rules or steps over and over. One single step is called an iterate.  Recursion. Given some starting information and a rule for how. Given some starting information and a rule for how to use it to get new information, the rule is then to use it to get new information, the rule is then repeated using the new information. repeated using the new information.

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

6. More Fractals in Nature

7. Complex Fractals

8. The Sierpinski Triangle Named after the Polish mathematician Waclaw Named after the Polish mathematician Waclaw Sierpinski 1916. Sierpinski 1916. It is one of the simplest fractal shapes in existence It is one of the simplest fractal shapes in existence It can be generated by infinitely repeating a procedure of connecting the midpoints of each side of the triangle to form four separate triangles, and cutting out the triangle in the center. It can be generated by infinitely repeating a procedure of connecting the midpoints of each side of the triangle to form four separate triangles, and cutting out the triangle in the center.

9. References http://www.dcet.k12.de.us/teach/quest/shari.h tm by Shari Galgano http://www.dcet.k12.de.us/teach/quest/shari.h tm by Shari Galgano http://www.dcet.k12.de.us/teach/quest/shari.h tm http://www.dcet.k12.de.us/teach/quest/shari.h tm http://math.rice.edu/~lanius/frac/ by Cynthia Lanius http://math.rice.edu/~lanius/frac/ by Cynthia Lanius http://math.rice.edu/~lanius/frac/ http://astronomy.swin.edu.au/~pbourke/fractal s/fuzzylogic/ by Roger Bagula http://astronomy.swin.edu.au/~pbourke/fractal s/fuzzylogic/ by Roger Bagula http://astronomy.swin.edu.au/~pbourke/fractal s/fuzzylogic/ http://astronomy.swin.edu.au/~pbourke/fractal s/fuzzylogic/ http://occawlonline.pearsoned.com/bookbind/p ubbooks/billstein_awl/medialib/shodor_site/les sons/frac1.html by The Shodor Education Foundation, Inc. http://occawlonline.pearsoned.com/bookbind/p ubbooks/billstein_awl/medialib/shodor_site/les sons/frac1.html by The Shodor Education Foundation, Inc. http://occawlonline.pearsoned.com/bookbind/p ubbooks/billstein_awl/medialib/shodor_site/les sons/frac1.html http://occawlonline.pearsoned.com/bookbind/p ubbooks/billstein_awl/medialib/shodor_site/les sons/frac1.html