Mathematics Field Days

For New England High School Students

Fractal Quiz!!!

1A. Here is a target for the chaos game. Using a sequence of A's, B's, and C's, explain how to move the seed into the INTERIOR! of the target in exactly 5 moves. For example, ABCCC means first do A, then do B, then do CCC. You might wish to use the chaos game software to experiment first. Click here to access this software. Please note that your browser must be JAVA enabled in order to use this program.

Enter the Sequence:

1B. Here is a second target.

Enter the Sequence:

2. Explain how we generated each of the following fractal images. Specifically, you need to provide

You might wish to use the software called "Fractalina" to experiment first. Click here to access this software. Please note that your browser must be JAVA enabled in order to use this program.

A.


Number of Vertices: Compression Ratio: Rotation:
B.


Number of Vertices: Compression Ratio: Rotation:
C.


Number of Vertices: Compression Ratio: Rotation:
D.


Number of Vertices: Compression Ratio: Rotation:
E.


Number of Vertices: Compression Ratio: Rotation:
F.


Number of Vertices: Compression Ratio: Rotation:
3. How did we make this animation? How many vertices in each frame? What is the compression ratio? In a brief paragraph, explain how the motion changes from frame to frame.

You might wish to use the software called "Franimate" to experiment first. Click here to access this software. Please note that your browser must be JAVA enabled in order to use this program. Also, when making movies with this software, be sure to use very few frames (like 6 or so) if your machine lacks a lot of memory.
4. Now how did we make this animation? How many vertices in each frame? What is the compression ratio? In a brief paragraph, explain how the motion changes from frame to frame.

For answers to these questions, click here after November 10.

BU Dynamical Systems and Technology Project