  High-redshift QSO spectra show large spatial fluctuations in the Ly-alpha
opacity of the intergalactic medium on surprisingly large scales at z>~5.5. We
present a radiative transfer simulation of cosmic reionization driven by
galaxies that reproduces this large scatter and the rapid evolution of the
Ly-alpha opacity distribution at 5<z<6. The simulation also reproduces the low
Thomson scattering optical depth reported by the latest CMB measurement and is
consistent with the observed short near-zones and strong red damping wings in
the highest-redshift QSOs. It also matches the rapid disappearance of observed
Ly-alpha emission by galaxies at z>~6. Reionization is complete at z=5.3 in our
model, and 50% of the volume of the Universe is ionized at z=7. Agreement with
the Ly-alpha forest data in such a late reionization model requires a rapid
evolution of the ionizing emissivity of galaxies that peaks at z~6.8. The late
end of reionization results in a large scatter in the photoionisation rate and
the neutral hydrogen fraction at redshifts as low as z<~5.5 with large residual
neutral 'islands' that can produce very long Gunn-Peterson troughs resembling
those seen in the data.
