@PeterTamaroff Mh. You take one extra $g_i$ per $n$, which instigates a (conceptual) mismatch; you can "fix" this by putting the two half triangles in one $g_i$.
@PeterTamaroff At some points, the $g_i$s will be wider than the $f_i$s they are in between. I think this is a bit ugly. But it does not fault the example, of course.
It's perfectly clear, but not as aesthetically appealing as possible. :)
@PeterTamaroff Yes, but since you take one $g_i$ more, there will be this mismatch (the $f_i$s having gone one level of width down, but the $g_i$s not yet).