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A \emph{thrackle} is a graph drawn in the plane so that every pair of itsedges meet exactly once, either at a common end vertex or in a proper crossing.Conway's thrackle conjecture states that the number of edges is at most thenumber of vertices. It is known that this conjecture holds for linearthrackles, i.e., when the edges are drawn as straight line segments.  We consider \emph{convex hull thrackles}, a recent generalization of linearthrackles from segments to convex hulls of subsets of points. We prove that ifthe points are in convex position then the number of convex hulls is at mostthe number of vertices, but in general there is a construction with one moreconvex hull. On the other hand, we prove that the number of convex hulls isalways at most twice the number of vertices.

Convex Hull Thrackles