The generalized entropy, calculated from the quadrat counts of the pop
ulation of the United States and Great Britain, is plotted against the
logarithm of the quadrat size. These graphs are linear over a range o
f scales that corresponds to the size of a city up to the size of the
country. This linearity indicates a strong scale-invariant component t
o the spatial population distribution pattern. Measurements of the gen
eralized q-dimensions and alpha spectrum of the spatial population dis
tribution patterns estimated from these graphs are presented.