# Chaos Under Control: Natural and Mathematical Fractls Lab

## David Peak and Michael Frame

A. Making natural fractals

Materials: six 3x3 squares of watercolor paper, two colors of fingerpaint

1. (Basic construction) Put a small amount of one color of fingerpaint on one square of paper, put a small amount of another color on another square. Place the squares together, paint side facing paint side. Press the squares together, flattening the paint between them. Pull the squares apart. After the paint has dried, tape them to a page in your lab notebook. Describe what you see. How are the paint patterns of the two squares related? How many levels of branching do you see?

2. (Iterated construction) Put a small amount of one color of fingerpaint on one square of paper, put a small amount of another color on another square. Place the squares together, paint side facing paint side. Press the squares together, flattening the paint between them. Pull the squares apart. Press the squares back together. Flatten them. Pull the squares apart. Repeat several times. Record the total number of times you flatten the squares together and pull them apart. (Five or six are good choices.) Pull the squares apart. After the paint has dried, tape them to a page in your lab notebook. Describe what you see. How are the paint patterns of the two squares related? How many levels of branching do you see? How are these patterns related to those you saw in 1?

3. (On your own) With your remaining two pieces of paper, design your own experiment, with the goal of testing how some aspect of the processing affects the fractal nature of the branching pattern. Put the results in your lab notebook and record your observations.

B. Making mathematical fractals

Materials: the "chaos game" window of TreenessEmerging

Deselect Draw Lines and Draw Vertices. Set Speed to maximum (100).

To set up for printing: Under the File Menu, select Page Setup. In the screen that appears, select "landscape" orientation:

1. (Basic construction) Set Scaling to 0.5. (Remember to press the return key if you type the scaling in the box below the slider.) In the window on the right,

* select the three vertices of a triangle by clicking the mouse cross-hairs at the points.

* Select the starting point by holding down the shift key and clicking the mouse.

* Click the Run button.

* Click the Run button.