We examine the evolution of intrinsic u-r colours of galaxies in the EAGLE cosmological hydrodynamical simulations, which has been shown to reproduce the observed redshift z=0.1 colour-magnitude distribution well. The median u-r of star-forming ('blue cloud') galaxies reddens by 1 mag from z=2 to 0 at fixed stellar mass, as their specific star formation rates decrease with time. A red sequence starts to build-up around z=1, due to the quenching of low-mass satellite galaxies at the faint end, and due to the quenching of more massive central galaxies by their active galactic nuclei (AGN) at the bright end. This leaves a dearth of intermediate-mass red sequence galaxies at z=1, which is mostly filled in by z=0. We quantify the time-scales of colour transition due to satellite and AGN quenching, finding that most galaxies spend less than 2 Gyr in the 'green valley'. On examining the trajectories of galaxies in a colour-stellar mass diagram, we identify three characteristic tracks that galaxies follow (quiescently star-forming, quenching and rejuvenating galaxies) and quantify the fraction of galaxies that follow each track.
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