Name ______
Fractals Project –
Due on March 20, 2014
Mark Goodwin from Antioch University, Seattle, designs this WebQuest.
This Web Quest introduces the power and beauty of fractal geometry.
Find the Web Quest at this address: http://questgarden.com/105/05/2/100614104745/evaluation.htm
It is focused on general concepts and practical applications.
Instructions:
Follow each task, watch the videos, fill out the worksheets and prepare a project poster board (may use the ones in the back of my room) presenting this project
(Left side of the board)
Introduction
Importance of fractals
(Center of board)
Title
Pictures, fabrics, 3D materials
(Right side of board)
Conclusion
Spiritual Lesson
Besides the poster board, must present a report showing all the worksheets and all the information the poster is demonstrating. APA Style, Bibliography might use Bibme.com
Introduction
Euclid’s geometry dates to 300 B.C., but there is a comparatively new kind of geometry discovered around 1980 called “fractal geometry.” This Web Quest is designed to introduce you to the power and beauty of fractals—a different way of looking at the world around us. As you continue your education you may find this new way of thinking about your surroundings to be quite useful in your future studies or career plans.
TASK
Through hands-on learning and practical research you and your classmates will get a feel for fractals. There are three tasks for you in this Web Quest:
1) To find a unique fabric based on fractal geometry.
Nova Science Video
2) The entire class will start to watch the Nova Science program “Fractals: Hunting the Hidden Dimension” as an introduction to fractals. This can be viewed on the Internet at Nova. After viewing this video, you will fill out Worksheet 1.
FUN WITH FRACTALS: Worksheet 1
(use after watching Fractals: Hunting the Hidden Dimension)
Name:
1. Why is fractal geometry better than Euclidean geometry for describing natural features or objects?
2. What does “iteration” mean in a mathematical sense?
3. How are climate researchers using fractals in their work?
4. What do Hollywood special-effects have to do with fractals?
5. If you were going to design a building would you need to use fractal geometry? Explain.
6. Why are the human brain and the World Wide Web both considered to be fractals?
Part 2: The Sierpinski Triangle
3) This picture shows an example of a mathematically generated pattern known as a Sierpinski Triangle. Visit http://www.kidsmathgamesonline.com/pictures/sierpinskitriangle.html
and find 3 pictures, photos, images, orclip art related to Sierpinski Triangle.
Part 3: Patent Research
FUN WITH FRACTALS: Worksheet 2
(use during patent research project)
Names:
1. Find a patent application for a product or a concept which uses fractal geometry. List the title of the patent, the application number, and the date of patent (or application).
2. What is the product supposed to be useful for?
3. Do you think there is a market for this product? Explain.
4. Can you find examples of real products which use this idea?
5. Does the patent application have lots of mathematical equations and concepts included? Why or why not?
Part 4: Fractal Fabric Search
FUN WITH FRACTALS: Worksheet 3
(use after completion of fabric research project)
Name:
1. Why are fractals useful for textile designers?
2. What role do you think computers play in fractal fabric design?
3. Can you find a real garment that incorporates fractals? Take a picture and paste it in this document. If so where did you see it and what is its intended use?
4. Why would fractals work well for the design of camouflage garments?
5. Besides wearable garments, for what other consumer products might fractal patterns and artistic designs be useful?
Part 5: Colours of Infinity Video
For review, the class will start to watch Arthur C. Clarke’s “Colours of Infinity”. http://www.youtube.com/watch?v=YU5tonVT-RU
You will fill out Worksheet 4 (a reflection quiz) after viewing this video.
FUN WITH FRACTALS: Worksheet 4
(use after watching The Colours of Infinity)
Name:
1. When you “zoom in” on a fractal it is “self-similar.” Explain what this means.
2. Why is the universe considered to be a fractal?
3. Why did it take until 1980 for fractals to be mathematically discovered?
4. Why is Benoit Mandelbrot considered to be the father of fractal geometry?
5. What kinds of ancient art forms have patterns which appear to be fractal-like?
6. Why are the human brain and circulatory system both considered to be fractals?