## Introduction

Welcome to the world of fractals: a beautiful place where math, science, art, and technology collide!

During this project you will learn what a fractal is, how to make one, how to talk the language of fractals, how beautifully complex patterns emerge from very simple beginnings, and where fractals patterns exists in nature.

You will create a web page called "Fractals" on your class website and maintain journal entries (tag = "fractals") about your searches and discoveries.

Your web page will answer the following questions:

What are fractals and how are they described?  How do we recognize fractals?  How do we create fractals?  What has society (art, science, etc) gained by using fractals?  Using the important concepts of fractals, describe how you would create a "fractal" version of something other than lines or curves, i.e. sounds or complex shapes?

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## Process

#### Getting Started - Step 1

1.  Add a web page titled "Fractals" to your class website.
(Due September 3)

2.  Print out a copy of the Fractal WebQuest Checklist; add it to your binder; use it to keep track of your progress on these tasks.  Keep notes on the tasks you want to revisit.  This is a large assignment - keep organized!

3.  Remember to update your journal as you go along.  All journal entries related to this project should be tagged with the key "fractals".  You should have not fewer than five journal entries for this project.  Entries should include:
* interesting learnings;
* which websites you found helpful and not;
* your progress on the tasks - including parts that you are struggling with
(Due September 4:  First journal entry.  Answers the Questions:  What do I already know about fractals?  What do I want to know about fractals?
Note: Remainder of journal entries dues upon completion of project)

#### Define - Step 2

4.  Read the definition of fractal on at least three different websites listed under the resource section.  Under the heading "Definition", write your own definition - be sure to include the most important characteristics of fractals.  Use your own words to write this definition!
(Due September 8)

5.  Under a section called "Dictionary of Terms", include a dictionary of terms commonly used to describe or discuss fractals.  Include at least five (5) terms.  For each term:

a.  Include the definition from an online dictionary or credible reference on fractals. Be sure to include a reference to the dictionary from which you got the definition.

b.  Include references to at least two sites about fractals that use the word.  Please copy the sentence in which the word is used onto your website and add a link to the page where you found it.

(Due September 8)

#### Explore - Step 3

6.  Include under a heading called "People":          Find at least three (3) names commonly associated with fractals.  For each one:

a.  Write one to two sentences introducing the individual; be sure to include where and when they did their work and their primary area of study.
b.  Write two to three sentences on their contribution to the area of fractals.
c.  Include an image of a fractal associated with the individual.
(Due September 10)

7.  Create a heading called "Fractals in Nature".  Find at least five examples of fractals in nature.  For each one, provide a link to a website that includes a good image of the fractal behavior in that example.  You must use at least three DIFFERENT domains for these links!  (the domain is the part of the web address between http:// and the next / )
(Due September 10)

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(Calendar Note: September 11 will be spent exploring Google Earth.  Take whatever notes you will need to complete the next part of the project!)

#### Recognize & Examine - Step 4

8.  Open Google Earth.
Use the "Copy image" feature to paste 3 images at different zoom levels of the Alaska coast into your web page under a section titled "Coastline Fractals in Alaska".  You should choose images that do a nice job showing the similarity of the pattern at different magnifications.
(Due September 12)

9.  Directly beneath the images from #8, write a paragraph (5-7 sentences) discussing the similarities and differences between the images and the detail available at each magnification level.
(Due September 12)

#### Create - Step 5

10.  Use one of the programs listed under resources to generate your own fractal.  Be creative!  We'll be printing and displaying these in the classroom - so make yours original.  Display your creation on your web page.

(I need to play around a bit more with these sites to choose the best one for students to use and provide more complete instructions)

(Due September 16)

#### Analyze - Step 6

11.  Follow these steps:
a.  Watch the Mandlebrot videos below.
b.  Read this How-To.  It does a great job explaining how fractals are generated: http://www.shodor.org/master/fractal/software/snowflake/help_docs/how_sf_works.html
c.  Play with the Snowflake fractal generator: http://www.shodor.org/master/fractal/software/snowflake/
d.  Complete the Snowflake Worksheet.  Answer the questions as part of your journal entry for the Analyze section of the project.
e.  Create the heading "Snowflakes". Underneath it include:
1. A copy of your favorite creation using the snowflake generator to your web page.  This should be an original fractal and must involve moving more than one point on the line.
2.  Below the image, add a paragraph (5-7 sentences) describing the process of running an iteration of your fractal.  Your fractal and explanation should be original.
(Due September 18)

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#### Reflect - Step 7

12.  Add a journal entry reflecting on the websites you used during this project.  Which stood out as exception?  Why?  Name at least two characteristics of a quality, useful website.
(Due September 20)

13.  Add a journal entry reflecting on what you learned during this webquest.  What was the most interesting?  What are you still confused about?  What would you like to learn next?
(Due September 20)

#### Bring it Home - Step 8

14.  Choose a family member with whom to share your website.
a.  Before showing to them, record what they already know about fractals and if there are particular things they would like to know.
b.  Walk the family member through the site you created ( you may print the page(s) out and take them home if you do not have internet access ).  Discuss what you have learned and describe the process you went through to build the content and create the site.
c.  Ask your family member to provide feedback on your site - including how readable it is; how much they think they could learn from it; general thoughts.
d.  You may turn in the responses from your family member manually on paper or add them as journal entries.
(Due September 23)

#### Above and Beyond

15.  Visit:  http://www.shodor.org/interactivate/activities/Tortoise/
BEFORE you start running the race, record when you expect the hare to get in front of the tortoise.  Then start running the race and take notes on what happens.  Did the race go as you expected?  Why or why not?

16.  How does question 10 relate to fractals?

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## Resources

Excellent beginner introduction
Cynthia Lanius' Fractal Lesson: http://math.rice.edu/~lanius/frac/

Excellent introduction - beginner -> advanced
Fractals Unleashed: http://library.thinkquest.org/26242/full/index.html

Semi-advanced introduction to fractals
Suzanne Alejandre's Fractal Lesson: http://mathforum.org/alejandre/workshops/fractal/fractal3.html

Mary Ann Connors' Exploring Fractals: http://www.math.umass.edu/~mconnors/fractal/fractal.html

Advanced exploration on Mandlebrot
Studying Mandlebrot Fractals: http://forum.swarthmore.edu/alejandre/applet.mandlebrot.html

Fractal Tool Tutorial
Amazing Seattle Fractals: http://fractalarts.com/ASF/Tutor1.html

Still images

Sekino's Fractal Gallery: http://www.willamette.edu/~sekino/fractal/gallerymain.htm

Fractal World's Fractal Pictures: http://oak.kcsd.k12.pa.us/~projects/fractal/pics.html

http://spanky.triumf.ca/

Video