## 1-D Aggregation

Aggregation is another process that can be modeled using rotors. Here
the underlying graph has a vertex for each non-negative integer, and
for each vertex n there is an edge from n to n-1 and from n to n+1. In
the aggregation scenario, all vertices start out empty; once a bug
hits an empty vertex, the vertex is filled and it gets a normal rotor
on it. If the newly occupied vertex is on the left side of 0, the
vertex immediately to its left becomes occupied as well. During each
stage, a bug is added to the system at 0, and it walks until it
results in either one new occupied site (on the right) or two new
occupied sites (on the left). The ratio between the number of occupied
sites to the left of 0 and the number of occupied sites to the right
of 0 approaches the square root of 2. Models of this kind have been
studied by Levine and Propp.

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