An introduction to Fractals

Ginny BohmeTeachers’ Circle

March 3, 2011

Fractals Are SMART: Science, Math & Art! www.FractalFoundation.org

Nature

GeometryAlgebra

Lungs

Neurons

Self Similarity Seed~ initiator Iterative Process~ rule

10.00 cm

6.00 cm

D

B

C

A

4.00 cm

8.00 cm

GO

R F

Seed- Equilateral Triangle Iterative Process- Fold the top vertex to the

midpoint of the opposite side, Then unfold.

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments and

critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in

repeated reasoning.

1 unit

1 unit

1 unit

Biome Tree

***Sierpinski Triangle

Sierpinski Carpet

Koch Snowflake

Wikipedia zn+1 = zn2 + c

Over nearly seven decades, working with dozens of scientists, Dr. Mandelbrot contributed to the fields of geology, medicine, cosmology and engineering. He used the geometry of fractals to explain how galaxies cluster, how wheat prices change over time and how mammalian brains fold as they grow, among other phenomena. http://www.nytimes.com/2010/10/17/us/17mandelbrot.html

Complex Analytic Dynamics:Pierre Fatou (1878-1929)- iterative and recursive processesGaton Julia (1893-1978)- iteration of rational functions

Fractal Pack- educator's guide Cynthia Lanius Fractal Unit for Middle

School