Fractals Everywhere you look Overview History n Definition

Fractals Everywhere you look

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

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

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

Definition Geometric pattern reproduced on a smaller and smaller scale

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

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

Where on Earth would I use fractals o Key Word is Earth o 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 n Used widely in nature simulation, business, medical, and computer realated fields n Used to help understand geometry with any age group n