Begin with a set of four points in the real plane in general position. Add tothis collection the intersection of all lines through pairs of these points.Iterate. Ismailescu and Radoi\v{c}i\'{c} (2003) showed that the limiting set isdense in the plane. We give doubly exponential upper and lower bounds on thenumber of points at each stage. The proof employs a variant of theSzemer\'edi-Trotter Theorem and an analysis of the ``minimum degree'' of thegrowing configuration.
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机译：从一般位置的真实平面中的四个点开始。通过这些点对将所有线的交点添加到此集合中。 Ismailescu和Radoi \ v {c} i \'{c}（2003）表明，极限集在平面上是密集的。我们给每个阶段的点数加倍的指数上限和下限。该证明采用了Szemer'edi-Trotter定理的变体，并分析了生长构型的``最小度''。
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