Angular correlation functions for an arbitrary number of partons are d
erived from a recursive scheme in the double log approximation. For pa
rtons in a sideways cone we calculate the normalised multiplicity mome
nts and obtain the fractal dimension D(q)=[(q+1)/q]gamma0 where gamma0
= 6 square-root alpha(s)/pi is the anomalous dimension controlling th
e energy dependence of the total multiplicity. At very high energies t
hese observables scale according to a known function of a single varia
ble. A systematic approach to finite energies is presented.