Abstract
Given S 1 , a finite set of points in the plane, we define a sequence of point sets S i as follows: With S i already determined, let L i be the set of all the line segments connecting pairs of points of ⋃ j = 1 i S j , and let S i + 1 be the set of intersection points of those line segments in L i , which cross but do not overlap. We show that with the exception of some starting configurations the set of all crossing points ⋃ i = 1 ∞ S i is dense in a particular subset of the plane with nonempty interior. This region is the intersection of all closed half planes which contain all but at most one point from S 1 .
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