Monday March 3, 2014
Models of natural behavior can be described well by writing stories and drawing pictures. This problem concerns the behavior of particles colliding and "precipitating" in a container.
In this problem, a story is given. Your task is to draw a picture that accurately depicts the story. You must label the parts of the picture that would be important for someone writing a computer simulation. The story is written out below.

In a container, particles move randomly. For the sake of simplicity, we will assume particles move in 2 dimensions: left and right, and up and down. At each time step, each particle picks a random direction and tries to move in that direction. If a container wall blocks the particle's movement, the particle stays still. Similarly, a particle will also stay still if its movement is blocked by another particle. All of the particles who can move do so at the same time.

After all particles have moved, if any two particles are next to each other in the left/right direction, there is some percent chance that those particles will collide. Collided particles no longer move randomly. Instead, those particles move in only one direction: down. When the particles fall to the bottom of the container, they stay put and are called "precipitate".

As the precipitating particles are falling, any particles directly beneath them will collide with then and become precipitate particles. That is, they will also stop moving randomly and will only move downward. The percent chance of this kind of collision is 100 percent.

Your solution should consist of a clear, well-labelled picture.
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