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FRACTALS
Problems!
By
Nick
Test
Your Knowledge:
On this
page you test your knowledge of what you know about
fractals. If you entered this quiz, we will give you the
login and password to the Mac only download page. There
are 5 problems you get to test yourself on, but you need
to do the activities first! Type the answer in the text
fields. To get the Chaos Game, you do NOT need the
password. The downloads are Mac Only because Nick only
programs on a Mac.
Please
type your name:
Please
type your email so we can send
you
the download area pass:
1. If
you play the Chaos Game (see below), what famous fractal
does it make?
Chaos
Game:
MATERIALS:
8 1/2 by 11 in. paper and a pencil
1. When
you play the chaos game, you start with a triangle made
of three points. The triangle should take up the entire
paper.
2. Draw a
random point anywhere inside or outside of the triangle.
3. Make a
point half-way between one of the 3 points made for the
triangle and the one you randomly drew. This is 1
iteration.
4. Start
over using the midpoint you took as your new point. Pick
another point of the triangle and draw the midpoint
between it.
5. Repeat
as many times as needed. You can guess the fractal after
a while. Download the Chaos
Game
computer program that plays the game. This software runs
on Mac only.
2. To
get the real Koch Curve you would need to do an infinite
number of iterations. What is the length of the
real Koch curve, assuming that the starting line
is 1 unit long?
3.
What is the area of the Sierpinski Gasket after 3
iterations? Assume that the original triangle is equal to
1 square unit.
4.
What is the area of the real (infinitely repeated)
Sierpinski Gasket? Assume that the original triangle is
equal to 1 square unit.
The
trophy room is a place where you get your name published
with an picture award next to your name for the internet
community to admire!
Qualify
me to be in the Trophy Room (check the box):
If you
are a teacher and want to learn how to use this with your
lessons, Click
Here.
Click a
link to go to an activity
The
Sierpinski Gasket
Koch's
Curve
Build-A-Fractal
Contest
Problems
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