  In the first section we review recent results on the harmonic analysis of
fractals generated by iterated function systems with emphasis on spectral
duality. Classical harmonic analysis is typically based on groups whereas the
fractals are most often not groups. We show that nonetheless those fractals
that come from iteration of affine mappings in R^d have a spectral duality
which is instead based on approximation and a certain dual affine system on the
Fourier transform side. The present work is based on iteration of frame
estimates (which have been studied earlier for regions in R^d). Our emphasis is
on new results regarding the interplay between the limit-fractal on the one
hand, and on the other the corresponding regions in R^d which generate iterated
function systems of contractive affine mappings. As an application of our frame
results, we obtain a classification of a certain type of spectral pairs.
