Visualizing the beauty in physics and mathematics
We start with a three-dimensional lattice containing a seed particle in the middle. Next, we draw a sphere with a given radius around the particle, and place another particle on the surface of this sphere at some random angle and have it execute a random walk, restricted to vertical or horizontal jumps between lattice sites.
To make the model more realistic, we let the length of each step vary according to a random Gaussian distribution. If at some point during its random walk, the particle encounters another particle within one lattice spacing, they stick together and the walk terminates. If the particle passes outside the sphere from which it was released, it is lost forever. The process is repeated as often as desired.
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