  The bulk spectrum of a possible Chern insulator on a quasicrystalline lattice
is examined. The effect of being a 2D insulator seems to override any fractal
properties in the spectrum. We compute that the spectrum is either two
continuous bands, or that any gaps other than the main gap are small. After
making estimates on the spectrum, we deduce a finite system size, above which
the K-theory must coincide with the K-theory of the infinite system. Knowledge
of the spectrum and $K$-theory of the infinite-area system will control the
spectrum and K-theory of sufficiently large finite systems.
  The relation between finite volume $K$-theory and infinite volume Chern
numbers is only proven to begin, for the model under investigation here, for
systems on Hilbert space of dimension around 17 million. The real-space method
based on the Clifford spectrum allows for computing Chern numbers for systems
on Hilbert space of dimension around 2.7 million. New techniques in numerical
K-theory are used to equate the K-theory of systems of different sizes.
