HandsOn 13 - Growing a Pattern in the Laboratory

I. Introduction

II. Setting Up the Experiment

III. Doing the Experiment

IV. Data Analysis

Data Analysis

It is likely that the aggregate you grow does not appear to be a solid disk (most likely, they will look something like Figures 4.4 - 4.7). We want to measure the fractal dimension D of this aggregate. To estimate its dimension, we use the circle method, described in HandsOn 7. For the radius r of different circles, we substitute the approximate radius of the aggregate at different times during its growth. Instead of counting boxes inside a circle, we calculate the number N of copper atoms. If the deposit is a fractal, we expect that the number of copper atoms N within a radius r to be
N = crD,
where c remains constant as the fractal grows and D is the dimension of the pattern. If we take the logarithm of both sides of this equation we get
log N = log(crD) = D log r+log  c.
To make use of this equation to find the dimension D, you need to determine the radius r of the pattern at specific times during the growth and the total number N of copper atoms in the pattern at these times. You measured the radius directly several times during the experiment. But what about number N of copper atoms?

Before going further, discuss with your partners how you might measure the number of copper atoms that have been deposited at any time. Then read the following procedure:

Q4.9: Which is the "right'' value of the current to use for a given interval? The value at the beginning? The value at the end? Would it make sense to use the average?

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