  We introduce the first two simulations of the IllustrisTNG project, a next
generation of cosmological magnetohydrodynamical simulations, focusing on the
optical colors of galaxies. We explore TNG100, a rerun of the original
Illustris box, and TNG300, which includes 2x2500^3 resolution elements in a
volume twenty times larger. Here we present first results on the galaxy color
bimodality at low redshift. Accounting for the attenuation of stellar light by
dust, we compare the simulated (g-r) colors of 10^9 < M*/Msun < 10^12.5
galaxies to the observed distribution from the Sloan Digital Sky Survey (SDSS).
We find a striking improvement with respect to the original Illustris
simulation, as well as excellent quantitative agreement in comparison to the
observations, with a sharp transition in median color from blue to red at a
characteristic M* ~ 10^10.5 Msun. Investigating the build-up of the color-mass
plane and the formation of the red sequence, we demonstrate that the primary
driver of galaxy color transition in the TNG model is supermassive blackhole
feedback in its low-accretion state. Across the entire population we measure a
median color transition timescale dt_green of ~1.6 Gyr, a value which drops for
increasingly massive galaxies. We find signatures of the physical process of
quenching: at fixed stellar mass, redder galaxies have lower SFRs, gas
fractions, and gas metallicities; their stellar populations are also older and
their large-scale interstellar magnetic fields weaker than in bluer galaxies.
Finally, we measure the amount of stellar mass growth on the red sequence.
Galaxies with M* > 10^11 Msun which redden at z<1 accumulate on average ~25% of
their final z=0 mass post-reddening; at the same time, ~18% of such massive
galaxies acquire half or more of their final stellar mass while on the red
sequence.
