  We present an analysis of X-ray colour maps of the cores of clusters of
galaxies, formed from the ratios of counts in different X-ray bands. Our
technique groups pixels lying between contours in an adaptively-smoothed image
of a cluster. We select the contour levels to minimize the uncertainties in the
colour ratios, whilst preserving the structure of the object. We investigate
the spatial distributions of cooling gas and absorbing material for a sample of
33 X-ray bright clusters, many containing strong cooling flows, in archival
ROSAT PSPC data. We present colour maps of a sample of the clusters, in
addition to adaptively-smoothed images in different bands. Most of the cooling
flow clusters display little substructure, unlike several of the
non-cooling-flow clusters.
  We fitted an isothermal plasma model with galactic absorption and constant
metallicity to the mid-over-high energy colours in our clusters. Those clusters
with known strong cooling flows have inner contours which fit a significantly
lower temperature than the outer contours. Clusters in the sample without
strong cooling flows show no significant temperature variation. We also had to
increase the levels of absorbing material to fit the low-over-high colours at
the cluster centres. Our results provide more evidence that cooling flows
accumulate absorbing material. No evidence for increased absorption was found
for the non-cooling-flow clusters. [abridged]
