An Interactive WebQuest
Designed and Compiled by Lysa
Knight
Introduction
| Task | Process | Evaluation | Conclusion | Credits | Teacher
Page
Fractals
are one of the newest branches of mathematics.
Mathematicians from previous centuries believed that they must exist,
but they were not truly realized until the advent of the computer. Your quest will be to research the history of
fractals, understand the terms associated with them, the uses that are being
found for them, and create your own designs.
http://library.thinkquest.org/26242/full/
http://astronomy.swin.edu.au/~pbourke/fractals/
http://sprott.physics.wisc.edu/fractals.htm
http://www.math.umass.edu/~mconnors/fractal/fractal.html
http://www.jracademy.com/~jtucek/math/fractals.html
http://archives.math.utk.edu/topics/fractals.html
http://www.google.com/search?hl=en&lr=&q=fractal+images
http://www.softsource.com/fractal.html
http://spanky.triumf.ca/www/fractal-info/f-hist.htm
http://www.ga.k12.pa.us/academics/US/Math/Geometry/stwk00/griffith/history.htm
http://fractals.iut.u-bordeaux1.fr/jpl/history.html
http://math.youngzones.org/Fractal%20webpages/history_fractals.html
http://www.sunleitz.com/whatarefractals.html
http://en.wikipedia.org/wiki/Fractal_geometry
http://home.att.net/~fractalia/history.htm
http://www.fractovia.org/art/faq3.html
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Mandelbrot.html
http://ecademy.agnesscott.edu/~lriddle/ifs/kcurve/kcurve.htm
You will
explore this newest branch of mathematics and geometry – Fractals. You will become familiar with the terms
associated with these images. You will
investigate how fractals are generated on the computer and actually create
fractals of your own. You will discover
how fractals are being used in the real world today. You and your group will pick one topic
related to fractals and give a presentation to your class.
Individually
you will complete the Fractal packet.
This includes:
1. defining the
terms in the vocabulary section
2.
creating the Sierpinski triangle and answering the questions
3.
completing the Fractory Center
4.
completing the Computer Generated Fractal
5.
generating the Koch Snowflake
6.
creating the Paper Fractal by folding
7.
designing your own fractal by hand in the Design Center
As part
of a team you will complete two projects.
These include:
1.
imagining ways that fractals might be used in the future
2.
becoming experts on a particular topic of fractals
Vocabulary – Individual Task
By the time we
have finished with this unit you should have a working knowledge of the
following terms.
1. Define each of these terms in your fractal
packet:
Butterfly effect
Cantor set
Chaos theory
Converge
Critical points
Diverge
Feigenbaum’s
constant
Fractal attractor
Fractal dimension
Iteration
Julia set
Koch curve
Lorenze model
Mandelbrot set
Strange attractor
Sierpinski Triangle – Individual Task
1. Go to the site below and follow the
instructions to create the Sierpinski triangle.
The triangular grid paper is in your fractal packet.
2. On the same web page is the line: Answer some Math Questions on the
Sierpinski Triangle. Click on this link
and complete the questions by pasting the questions into a word document and
answering them.
The Fractory Center – Individual Task
1. Analyze the fractals you are viewing on the
different websites. Discuss the
similarities and difference between them.
2. Choose one of the fractals that you have
found other than the Mandelbrot or Julia.
What is the algorithm needed to generate the fractal that you chose?
3. What effect does altering the values in the
algorithm have on the fractal?
4. How does the choice of colors affect the
fractal?
5. Print the fractal out with its algorithm.
Computer Generated
Fractal – Individual Task
1. Use a program from the internet to generate
your own fractal. Remember color is an important
factor in your design.
http://www.lilavois.com/nick/fractals/index.html
http://www.pangloss.com/seidel/Frac/fgen.cgi
2. Print out your fractal and mount it to a piece
of colored construction paper that will enhance your fractal.
3. Write down or print out the values that you
substituted into the algorithm so that your fractal can be recreated. Place these on the back of your fractal.
4. Name your fractal. Place this on the back of the fractal also.
Koch Snowflake – Individual Task
1. Complete the worksheet in your packet that
explains how to create the Koch Snowflake fractal or go to the site below to
see how to create it.
2. Create a Koch Snowflake of 2 iterations on
plain computer paper. (The beginning
triangle is not an iteration).
Do not use the triangular template for this.
3. Optional
- 2 bonus point -.Color/shade the Snowflake and mount on a piece of construction
paper.
Paper Folding Fractal – Individual Task
1. Go to the sites below and discover how to
create a paper folding fractal.
2. Use the page in your packet to create this
fractal.
3. Fold and cut it and attach it to a piece of
construction paper as on the diagram site.
Design Center – Individual Task
1. Create your own fractal without the help of a
computer. That’s right! With a straight edge and compass, colored
pencils, etc…the way Euclid would have done it!
2. You may look at computer generated designs
for inspiration but the final product must be your own creation.
3. This should be done on a piece of plain
computer paper.
4. Remember choice of color is important in the
design of your fractal.
5. Mount it on a piece of colored construction
paper
Reality Center – Group Project
2. Suggest a new way to use fractals that might
eventually become a reality.
a. Design a way to
implement your plan. Be specific in the
type you would use and the purpose.
b. Illustrate the type of
fractal you are discussing. This should
be included in your PowerPoint presentation.
3. Create a PowerPoint presentation with at least
10 slides conveying this information and title it Fractal Uses.
Fractal Experts – Group Project
1. Your group will be given one topic that must
be completed and presented to the class.
Everyone in the group must participate in the development and the actual
presentation.
2. Your group will create a note sheet for
students that will accompany a 10 slide PowerPoint presentation.
3. Your group will design a 5 question quiz with
a separate answer sheet based on the information that you present to the
class. You will provide paper copies for
each student.
Team A - Historians
Your
team has the responsibility to investigate the history of fractals.
1. When were fractals first
realized?
2. Who is responsible for the
term “fractals”? Did anyone have any of
these ideas before him?
3. What type of advancement has
been made in the field of fractals since they were realized?
Team B - Mathematicians
Your team has the responsibility to investigate fractals mathematically.
1.
What mathematics and devices are needed to produce
fractals?
2.
Give an example of a formula that produces a fractal
and show the fractal it produces.
3. What is an
iteration?
Team
C – Application
Experts
Your
team will investigate practical uses of fractals.
1. Using the resources from the internet,
find at least eight different ways to use fractals in the real world.
2. Describe the types or models
that are used for these purposes.
3. Choose one of the uses and
investigate it fully and report on your findings.
Team
D – Art/Music Experts
Your
team will investigate fractals as art and in music.
1. What medium is used to
produce fractal art and fractal music?
2. Who are some fractal
artists/composers? (Name at least three.) Are they artists or mathematicians?
3. Find at least two fractal
drawings and two examples of fractal music. Make a link to them in your
PowerPoint presentation.
You will
be graded on your Fractal Packet and on your group presentations. For group presentations, click the link below
for the rubric.
This site
was designed so that you could experience the beginnings of a new branch of
mathematics. Fractals constitute a brand
new field of geometry that enables mathematicians to describe figures and
shapes in ways that were not possible before.
The realm of possibilities that are opening up for the uses of fractals
seems infinite – much like fractals themselves.
I hope you have enjoyed your journey into this exciting new world!
Special
Thanks
Keith Bolstein, Technology Department Lake Highland
Preparatory School
Benoit Mandelbrot – Creator of Fractals
Lake Highland Preparatory School - Honors Geometry
Students (2005-2006)
We all benefit by
being generous with our work. Permission
is hereby granted for other educators to copy this WebQuest, update or
otherwise modify it, and post it elsewhere provided that the original author's
name is retained along with a link back to the original URL of this WebQuest.
On the line after the original author's name, you may add Modified by (your
name) on (date). If you do modify it, please let me know lknight@lhps.org and provide the new URL.
Last updated 5/2/06. Based on a template from The WebQuest Page