  The Kruskal-Katona theorem together with a theorem of Razborov determine the
closure of the set of points defined by the homomorphism density of the edge
and the triangle in finite graphs. The boundary of this region is a countable
union of algebraic curves, and in particular, it is almost everywhere
differentiable. One can more generally consider the region defined by the
homomorphism densities of a list of given graphs, and ask whether the boundary
is as well-behaved as in the case of the triangle and the edge. Towards
answering this question in the negative, we construct examples which show that
the restrictions of the boundary to certain hyperplanes can have nowhere
differentiable parts.
