SimuLab 13: Measuring the Computer-Generated Aggregation Pattern

You need the Fractal Dimensions program to complete this SimuLab. Download it here.	Download Fractal Dimensions:
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	Mac OS 7.x	Windows 95/98/NT/2000

Close the Aggregation Kit program and call up the Fractal Dimension program. Bring up the pattern you saved from the Aggregation Kit and measure its dimension using the box method. If you saved an image from the Straight setting of walker motion, call that up and measure its dimension also.

The Fractal Dimension program offers a second way to measure the dimension of an object, the so-called circle method of HandsOn 2.2. Try out this second measurement method on your computer-generated pattern.

1. Click in the center of your pattern to set the center of the circles you are about to have the computer draw.


2. Click on the circle icon, second from the left in the toolbar. The computer counts the number of pixels inside the circle of that radius. (Pixels are the small dots that form the images on a computer screen.)


3. Now change the radius of the circle using the size tool at the top of the window. Click on the circle tool to count the pixels inside the new circle.


4. Select several more radii and have the computer count pixels for these circles also.


5. Click on the graph and data tools. You may want to choose additional values of the radius, so that points are more or less evenly spaced along the graph. Click on entries in the "# pixels'' column of the table to discard points you do not want included in the graphical measurement of the slope.


6. You may want to use the circle method to re-measure the dimension of your saved coastline or the image saved from the electrodeposition experiment, comparing these measures of dimension to those obtained using the box method. To do this quickly, click on the fast circle icon, fourth from the left in the toolbar.

Q4.16: Do you get the same dimension using the circle method as using the box method?

Q4.17: Which settings of the Aggregation Kit program can produce a pattern with a fractal dimension near to that of the pattern from the electrodeposition experiment: the Straight setting or the Random setting for the way the walker moves?

Q4.18: There is always some difference between the dimension of the pattern grown in the electrodeposition experiment and the pattern grown with the Aggregation Kit. What does this difference mean? How large a difference is acceptable if the Aggregation Kit model of fractal growth is to be accepted?

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