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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