Spring 2001 Chaos and Fractals
Resources

General	Week 1	Week 2	Week 3
Week 4	Week 5	Programs

General Fractal and Chaos Resources

Dynamical Systems and Technology Project - this is where the books we use came from

Center for Polymer Studies at BU - an excellent site that shows real live fractals and chaos. Good hands on activities too.

Fractal Frequently Asked Questions and Answers

Fractals Unleashed - excellent descriptions and examples in the tutorial section

The Chaos Experience - good real world examples of chaos

The Chaos Metalink - links to every conceivable chaos related site

Week 1: Geometric Iteration

Cynthia Lanius' Lessons: A Fractals Lesson
This is Beth's new favorite fractal site! This was written for elementary/middle school students but the questions are not as trivial as they seem. Can you work them out? You must visit Sierpinski's Gasket - especially Sierpinski meets Pascal and Jurassic Park Fractal - go through all the pages it's worth it.

Fractal Modeling Tools from the Shodor Foundation
Manipulate the rules for Koch's Curve and Sierpinski's Gasket to create new fractals in this easy to use Applet.

Animated Fractals from the Chaos Experience
Look at these animated fractals. Can you figure out the iteration rules for each of them?

Week 2: Self-Similarity

Self-Similarity in Mathematics and Nature
A lesson plan using the snowflake applet to investigate self similarity.

Cynthia Lanius' Lessons: A Fractals Lesson - Self Simliarity
Try the activities in this 'chapter' You can use the triangle graph paper here.

Week 3: Random Fractals

Play the Chaos Game from the Dynamical Systems and Technology Project
After you've played the game visit Chaos in the Classroom and find out how it works

The Center for Polymer Studies' Java Applets demonstrate random patterns in nature as well as the Dance of Chance museum exhibit

Fractalina lets you manipulate the rules of the chaos game to create new patterns

Look at these cool pictures of randomly generated fractals at Random Fractals.

Week 4: Fractional Dimension

A description of Fractional Dimension from the Science House has several images to analyze using the Fractional Dimension program from the Polymer Center (see the programs below)

Week 5: Natural Fractals

Hele Shaw Viscous Fingering from the Center for Polymer Studies
We will do this experiment during this session. What variables can you think of to investigate?

Free Programs to Download

Graphic Converter - A drawing program that can be used for most of the activities the first couple of weeks. This is shareware so you should register it and pay the very low cost.

Programs from the Center for Polymer Studies

To download the programs follow the directions on the program page. These are all excellent programs, but the ones we will most likely use include:

The Fractal Dimension program gives the student a variety of objects to measure to determine their dimension. The program offers two measuring methods: (1) the box method which covers the object with different sized boxes and records the number of boxes it takes to cover the object; and (2) the circle method which covers the object with concentric circles and records how much of the object is within each circle. The program graphs the results of its measurements and allows the student to choose which data points they want the computer to graph. Objects from the "real world" (including patterns grown in laboratory experiments) can be scanned into the computer and imported into this program for analysis.

The Aggregation Kit program automates the student hands-on activity of pattern building. The student can generate computer aggregates by setting a number of variables. The program allows the student to split screens an observe two aggregates at once in order to determine the effect that changing variables has on the aggregate that grows. Aggregates generated by this program can be saved and transferred into the Fractal Dimension program to be analyzed.

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