  We use the Fourth Data Release of the Sloan Digital Sky Survey to investigate
the relation between galaxy rest frame u-r colour, morphology, as described by
the concentration and Sersic indices, and environmental density, for a sample
of 79,553 galaxies at z < ~0.1. We split the samples according to density and
luminosity and recover the expected bimodal distribution in the
colour-morphology plane, shown especially clearly by this subsampling. We
quantify the bimodality by a sum of two Gaussians on the colour and morphology
axes and show that, for the red/early-type population both colour and
morphology do not change significantly as a function of density. For the
blue/late-type population, with increasing density the colour becomes redder
but the morphology again does not change significantly. Both populations become
monotonically redder and of earlier type with increasing luminosity. There is
no significant qualitative difference between the behaviour of the two
morphological measures. We supplement the morphological sample with 13,655
galaxies assigned Hubble types by an artificial neural network. We find,
however, that the resulting distribution is less well described by two
Gaussians. Therefore, there are either more than two significant morphological
populations, physical processes not seen in colour space, or the Hubble type,
particularly the different subtypes of spirals Sa-Sd, has an irreducible
fuzziness when related to environmental density. For each of the three measures
of morphology, on removing the density relation due to it, we recover a strong
residual relation in colour. However, on similarly removing the colour-density
relation there is no evidence for a residual relation due to morphology.
[Abridged]
