1. Fractals
Everywhere you look

2. Overview History Definition of Fractals Fractal Application
Fractals in the classroom
NCTM Standards

3. A Brief history Before Mandelbrot Benoit Mandelbrot Flooding of Nile
Economics
Brownian Motion
Benoit Mandelbrot
Electronic noise
"How Long Is the Coast of Britain?"

4. What is “a fractal” Euclidean Shapes Fractal Shapes Square Circle
Triangle
Fractal Shapes
Coastline
Snowflake
Rivers
Nerve Cells

5. Definition
Geometric pattern reproduced on a smaller and smaller scale

6. Koch Snowflake Iterations Self Similar Exact Statistical
Exact copy of original
Snowflake
Statistical
Only looks alike under magnification

7. How long is the coast of Britain
As size decreases accuracy increases
As size decreases total distance increases indefinitely

8. Where on Earth would I use fractals
Key Word is Earth
Nature simulation

9. Snowflake Iteration

10. Why Study Measuring Crop Roots Chromosomes DNA Sequences
Soil Structure
Stock market timing
Computer Science
Telecommunications
Surface Physics

11. Bringing Fractals Into the Classroom
Older Ages
Demonstrate the nature of fractals
Younger Ages
Koch Snowflake construction
Similar shapes

12. NCTM Standards Rational Number Concepts Proportionality Measurement
Transformations
Visualization

13. Wrap Up
Fractals are Geometric pattern reproduced on a smaller and smaller scale
Used widely in nature simulation, business, medical, and computer realated fields
Used to help understand geometry with any age group