  We formulate the angular structure of Lacunarity in fractals, in terms of a
symmetry reduction of the three point correlation function. This provides a
rich probe of universality, and first measurements yield new evidence in
support of the equivalence between self-avoiding walks and percolation
perimeters in two dimensions.
  We argue the Lacunarity reveals much of the Renormalisation Group in real
space. This is supported by exact calculations for Random Walks and measured
data for percolation clusters and SAW's. Relationships follow between exponents
governing inwards and outwards propagating perturbations, and we also find a
very general test for the contribution of long range interactions.
