The fraction of galaxies with red colours depends sensitively on environment, and on the way in which environment is measured. To distinguish competing theories for the quenching of star formation, a robust and complete description of environment is required, to be applied to a large sample of galaxies. The environment of galaxies can be described using the density field of neighbours on multiple scales - the multiscale density field. We are using the Millennium simulation and a simple HOD prescription which describes the multiscale density field of Sloan Digital Sky Survey DR7 galaxies to investigate the dependence of the fraction of red galaxies on the environment. Using a volume limited sample where we have sufficient galaxies in narrow density bins, we have more dynamic range in halo mass and density for satellite galaxies than for central galaxies. Therefore we model the red fraction of central galaxies as a constant while we use a functional form to describe the red fraction of satellites as a function of halo mass which allows us to distinguish a sharp from a gradual transition. While it is clear that the data can only be explained by a gradual transition, an analysis of the multiscale density field on different scales suggests that colour segregation within the haloes is needed to explain the results. We also rule out a sharp transition for central galaxies, within the halo mass range sampled. ; Comment: 24 pages, 21 figures, accepted for publication by MNRAS