Fractals Everywhere you look

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

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

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

Definition Geometric pattern reproduced on a smaller and smaller scale

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

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

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

Snowflake Iteration

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

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

NCTM Standards Rational Number Concepts Proportionality Measurement Transformations Visualization

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