2004 Project Description
Sketchpad and Fractals
(Worksheet and GSP instructions)
Internet Research Guide
- Open this document and then you'll
have a copy of this worksheet to fill in as you find the
answers.
Fractal Internet Worksheet.doc
(Word Document)
- Save it to your disk or store it
temporarily on the H:\ drive in a folder with your name on it.
- Print a copy of your completed
worksheet when you are done to turn in!
Getting
Started: Go to this site and read this tutorial (it may not work on Friday 1/31)
http://www.techlar.com/fractals/websys.exe?file=explore/tutorials/kids10a.html
Now review a little with these few pages and then take the quiz. (it
may not work on Friday 1/31)
http://library.thinkquest.org/26242/kids/index.html
How did you do?
Using
the following Web sites, define each of the following terms:
What is a fractal?
1.
http://mathforum.org/alejandre/workshops/fractal/fractal3.html
2.
So, what
are fractals?
- Fractal
- _________________________________________________
What does it mean for a shape to be self-similar?
3.
Strictly
Self-similar shapes
4.
http://astronomy.swin.edu.au/~pbourke/fractals/selfsimilar/
Self-similar -
_____________________________________________
What is dimension?
What is the dimension of a
geometric object?
6.
Mathematical
Interpretation
- Dimension
of a geometric object - ________________________________________________
Dimension of a Fractal?
7.
http://math.rice.edu/~lanius/fractals/dim.html
Cynthia
Lanius on Fractal Dimension
http://math.bu.edu/DYSYS/chaos-game/node6.html#SECTION00060000000000000000
Robert Devaney on Fractal Dimension
Non-integer
and integer dimensions
- Dimension
of a fractal - ________________________________________________
What
is iteration?
8.
http://math.rice.edu/~lanius/fractals/iter.html
Cynthia Lanius on Iteration
- Iteration - ___________________________
Given the following
equation and seed, what are the results of the next four iterations of the
equation?
y = 5x – 4;
x0 =
2 (2 is the seed of this iteration)
- x1
= 5(2) – 4 = 6
- x2
= 5(6) – 4 = 26
- x3
= 5(26) - 4 = 126
- x4
=
- x5
=
- x6
=
- x7
=
Since 2 is considered the seed of
this iteration, how would you describe the seed?
- Seed
- ___________________________________________________
9.
http://members.tripod.com/~mschreier/english/fracappl.html
List five real-world applications of fractals:
1)
________________________________________________________
2)
________________________________________________________
3)
________________________________________________________
4)
________________________________________________________
5)
________________________________________________________
10.
http://math.bu.edu/DYSYS/index.html
Bob Devaney’s BU website with lots of info
11. http://www.ealnet.com/ealsoft/recursio.htm
List the names of three famous fractals and ways that you
can remember what they look like:
1)
__________________________________________________________________
2)
__________________________________________________________________
3)
__________________________________________________________________
http://members.tripod.com/~mschreier/english/fracback.html
List three people who were/are important in the study of
fractals and explain their work with fractals:
1)
_______________________________________________________________________
2)
_______________________________________________________________________
3)
_______________________________________________________________________
http://archive.ncsa.uiuc.edu/Edu/Fractal/Fvisual.html
Describe the method used to color
fractals such as the Mandelbrot or Julia sets.
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