7+Fractals

PBS video: Hunting the Hidden Dimension - we own it - start with that? or do a section at a time followed by exploration activities

Day 1: Intro to Fractals: What are they? Where do we find them? watch bit of video (20 minutes or so) discuss main aspects of definition: self-similarity, recursion, upload a pic of you and a fractal!

Day 2: Geometric Fractals - Exploration & Findings practice drawing geometric fractals - Sierpinski's Triangle and Koch snowflake - show different stages Vi Hart video on doodling in math class - how binary trees can make Sierpinski's triangle Chaos Game & Sierpinski's Triangle: http://www.shodor.org/interactivate/activities/TheChaosGame/ Leap Fractal Game using chaos game fact to hit a target by going halfway to vertex of triangle go from easy - hard, let students choose

Day 3: Taking it to 3-D, Introduce Fractal Dimension Geometric Fractals - created by a physical iteration of something done to a starting shape Sierpinski's Triangle or Square, Koch Snowflake, Dragon, Cantor dust, 2-D vs. 3-D, lots of making! in both 2d and 3d explore perimeter (3d surface area) and area (3d volume)

Complex Function - created by iterating a complex function and color coding behavior short lesson on complex numbers represented in 2-d on graph

Mandelbrot, Julia: http://www.shodor.org/interactivate/lessons/TheMandelbrotSet/

'coloring book' activity to begin to understand how Mandelbrot set is defined/determined fractals in nature - connection to fibonacci vi hart videos

Fractals in Art Hokusai, Escher

use betty's project stuff as a starting point

Calculating Dimensions Explanation: http://www.shodor.org/interactivate/discussions/DimensionAndScale/

Line deformation fractals explanation & applet: http://www.shodor.org/interactivate/activities/FlakeMaker/

online Fractals course - parts are advanced, but good resource @http://library.thinkquest.org/26242/so much stuff on fractals - good explanations of dimension Lanius Fractal page lessons Fractal Arts page with tools to make your own fractals BU/Museum of Science page re: fractal research in real life

file for looking at sierpinski's triangle - needs editing, but explores perimeter and area, use limits draw sierpinski's in sketchpad?