deletions | additions       diff --git a/Circle .tex b/Circle .tex  index b465254..44ee01d 100644  --- a/Circle .tex  +++ b/Circle .tex 
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\section{Sphere generation}  Shot configurations were evaluated for $1$ shot up to $4$ shots. Beyond $4$ shots the algorithm becomes significantly less efficient. This efficiency problem is discussed in the following section.  In general, for a configuration of $n$ shots, each with a randomly chosen radius of $r$ (for $r={4,8,14,18}$), shots were placed randomly on the square lattice. For each generation of the genetic algorithm, one shot was chosen randomly and "mutated" in either radius length or in position.  Each shot was modeled as a random walk. Like with SAW, a this random walk is a mathematical formalization of a path that consists of a succession of random steps. In this application, however, the constraint is not that two separate steps cannot coincide; rather, two separate circles cannot coincide.