  We study a model of scalar quantum field theory in which space-time is a
discrete set of points obtained by repeatedly subdividing a triangle into three
triangles at the centroid. By integrating out the field variable at the
centroid we get a renormalized action on the original triangle. The exact
renormalization map between the angles of the triangles is obtained as well. A
fixed point of this map happens to be the cotangent formula of Finite Element
Method which approximates the Laplacian in two dimensions.
