Let's start to experiment:

Here is a procedure for an equilateral triangle:

to equi :s
repeat 3[fd :s rt 120]
end
Now I think that I might be able to tile the plan by putting enough triangles together as a basic unit turning a bit and repeating myself so let's see:

to Pat1 :r :p :s
repeat :r [repeat :p[ equi :s rt 60]]
fd :s
end

Well Pat1 10 4 20 just gives a hexagon - so would Pat1 6 4 20 of course.
I might experiment a little more with the variables but perhaps just turning right 60 after every triangle is a bit predictable. How about:

to Pat2 :r :p :s
repeat :r [repeat :p[ equi :s rt 60 fd :s] repeat :p [equi :s lt 60 fd :s]]
end

That is slightly more interesting but a bit ad hoc. Hope you are getting an idea though ...