  The measure supported on the Cantor-4 set constructed by Jorgensen-Pedersen
is known to have a Fourier basis, i.e. that it possess a sequence of
exponentials which form an orthonormal basis. We construct Fourier frames for
this measure via a dilation theory type construction. We expand the Cantor-4
set to a 2 dimensional fractal which admits a representation of a Cuntz
algebra. Using the action of this algebra, an orthonormal set is generated on
the larger fractal, which is then projected onto the Cantor-4 set to produce a
Fourier frame.
