  We study the spectral properties of a fractal VNLE obtained from the standard
Vicsek set VS by making a countable number of identifications of points so that
all the line segments in VS become circles in VNLE. We show that the standard
Laplacian on VNLE satisfies spectral decimation with the same cubic
renormalization polynomial as for VS, and thereby give a complete description
of all eigenfunctions of the Laplacian. We then study the restrictions of
eigenfunctions to the large circles in VNLE and prove that these are Lipschitz
functions.
