1. Fractals What are fractals? Who is Benoit Mandlebrot? How can you recognize a fractal pattern? Who is Waclaw Sierpinski?

2. What are fractals? A fractal is a pattern that is self-similar. When magnified, small parts of a self- similar figure cannot be distinguished from the whole figure.

3. Benoit Mandelbrot Benoit Mandelbrot was born in 1924 in Warsaw and moved to the US in 1958. He is known as the “father of fractals. He is a mathematics professor and researcher. He made many important discoveries in the field of fractals during the 1970’s and 1980’s. In 1982 he connected mathematics and nature through fractal geometry.

4. Fractals in Nature Some natural objects that approximate fractals include: Clouds Mountain ranges Lightning bolts Snowflakes Broccoli & cauliflower Crystals Trees and ferns

5. Waclaw Sierpinski 1882-1969 Waclaw Sierpinski was born in 1882 in Warsaw, Poland. He was a professor of mathematics at the University of Lvov, the University of Moscow, and the University of Warsaw. He invented the Sierpinski Gasket.

6. The making of a Sierpinski Gasket 1. Take your equilateral triangle and find the midpoint of each side. Connect the midpoints. (Stage 1)

7. The making of a Sierpinski Gasket 2. Find the midpoint of each side of the three outside triangle and connect the midpoints. (Stage 2)

8. The making of a Sierpinski Gasket 3. Find the midpoint of each side of the nine outside triangle and connect the midpoints. (Stage 3)

9. Creating a Fractal Card Step 2 Step 3 Step 4 …

10. Fractal Construction

11. Fractal Figures Let’s look a making some other fractal figures. http://www.hbschool.com/activity/elab2004/g r6/21.html

12. Van Kock Curve

13. Lines Fractal

14. Julia Phoenix

15. Pentagon Fractal http://www.coolmath.com/fractals/gallery.htm

16. What are fractals? A fractal is a pattern that is self-similar. When magnified, small parts of a self-similar figure cannot be distinguished from the whole figure. Who is Benoit Mandlebrot? He is known as the “father of fractals. How can you recognize a fractal pattern? When magnified, small parts of a self-similar figure cannot be distinguished from the whole figure. Who is Waclaw Sierpinski? He invented the Sierpinski Gasket (triangles in triangles).