Abstract: The following model was proposed by Stefan Steinerberger.Consider the convex hull of a collection of disjoint open discs withidentical radii. The boundary of the convex hull consists of a finitenumber of line segments and arcs. Randomly (uniformly) choose a pointin one of the arcs in the boundary. Attach a new disc at the chosenpoint so that it is outside of the convex hull and tangential to itsboundary. Replace the original convex hull with the convex hull of allpreexisting discs and the new disc. Continue in the same manner. Simulations show that disc clusters form long, straight, or slightlycurved filaments with many small side branches and occasionalmacroscopic side branches. For a large number of discs, the shape ofthe convex hull is either an equilateral triangle or a quadrangle.Side branches play the role analogous to avalanches in sandpilemodels, one of the best-known examples of self-organized criticality(SOC). Simulation and theoretical results indicate that the size of abranch obeys a power law, as expected of avalanches in sandpile modelsand similar ``catastrophes'' in other SOC models.