  We consider the problem of reconstructing a compactly supported function from
samples of its Fourier transform taken along a spiral. We determine the Nyquist
sampling rate in terms of the density of the spiral and show that below this
rate spirals suffer from an approximate form of aliasing. This sets a limit to
the amount of undersampling that compressible signals admit when sampled along
spirals. More precisely, we derive a lower bound on the condition number for
the reconstruction of functions of bounded variation, and for functions that
are sparse in the Haar wavelet basis.
