The main points are:
1. Horizontal, vertical, and 45 degree angle transitions (for which you need two tiles for each 45 degree angle, since they have to cross the boundary in the middle)
|____ |____ |
(if that shows up right). Your angle goes from one period to the other (the bottom center of the left tile to the top center of the right tile).
You have four sets like that, and then your normal horizontal and vertical tiles. 12 tiles total for the transitions.
2. Make the tiles small. The smaller they are, the smoother your curves by mixing different kinds of edges.
3. Make the transitions as chaotic as possible (lots of grass or dirt "noise" overlapping the transition), which hides the fact that you only have straight and 45 degree angles.
4. Mix and match random alt-tiles in order to hide the repetition in the chaotic tiles.