1. 12-1A 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 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
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. Fractal Construction

10. Fractal Figures Let’s look a making some other fractal figures.

11. Van Kock Curve

12. Lines Fractal

13. Julia Phoenix

14. Pentagon Fractal

15. 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).

16. Assignment 12-1A
Page 752, 1, 2, 4, 20, 22