HandsOn 14 - Building an Aggregate by Hand

Figure shows a large random aggregation pattern. This pattern was grown using the random walk you are about to use. Your job is to start a random walker on the rim of the surrounding circle. Then let the walker stagger around the grid until it reaches the black pattern. When the walker reaches the black pattern, it sticks and becomes a black square. Then another walker starts from a random point on the rim of the surrounding circle and staggers around until it sticks to the pattern. And so forth. That's all there is to our model. This model is called diffusion-limited aggregation, or DLA for short and comes from the fact that the growth rate of the pattern depends on the rate at which particles arrive at the surface by diffusion (the net motion due to their random walk).


Figure 4.8: An aggregation resulting from a random-walk model. This pattern was built from a single "seed'' (black square with white dot) by releasing 170 random walkers, one at a time, from the rim of the surrounding circle and allowing each to walk until it reaches and sticks to the growing pattern.

Q4.10: Do you think that the electrodeposition experiment can be described using this model? Discuss why or why not.

Carry out the following activity using simple linear graph paper.


Figure 4.9: Randomly-generated table of steps up, down, left, and right (U, D, L, R). Read a line of letters from the table to direct your 2-D walker.

Q4.11: Compare your results to those of others in the class. Are the new squares mostly added near the ends of the spidery legs or near the center of the existing pattern? Why should this be? Can you think of a simple explanation?

Q4.12: Compare this model to your picture of the motion of ions in the electrodeposition experiment. What component of the experiment does the walker represent? What component does the black pattern represent?

Q4.13: Who or what is doing the "die throwing'' in the electrodeposition experiment? In what way do the ions in the electrodeposition experiment move differently than the walker in the aggregation model?


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