Tried seeing how small of a program I could fill the screen with. Came up with this, but feels like there has to be a more elegant solution ^^;
[[[[[[[[[[[[[[[[F]]]]]]]]RRF[[R]R]]]]]]]]]
[[[[[[[[[[[[[[[[F]]]]]]]]RRF[[R]R]]]]]]]]]
[[[[[[[[[[[[[[[FF]]]]]]]RRF[RRR]]]]]]]]]
I then found a solution in 37 which uses a slightly different approach (namely, create a pattern that spans the full X and Y output space, then shift it by one step each iteration): [[[[[[[[[[[[[[[[FFF]]]]]R]]]F]]]]]]]]