New DL Background

Considering a mixing of all colors is technically brown, you won't get a "pretty" shade for tri-color by just mixing.

You could just play around with sweeping gradient effects by going from white through grey to black in different arrangements.
Example: sweeping gradient from top left to bottom right starting at white in the top corner and ending in black in the bottom corner.
There's also swirl, wave, line (horizontal, vertiacal, intersecting, etc.), kaleidoscope, etc. Just look at some classic art (the ones without anything in them, just color patterns) for ideas.