Splatmapping / blending between two textures in an atlas?

I have not properly experimented with this yet however I want to produce a simple blend between a grid of squares in the same mesh, procedurally generated. I have been looking into splat maps but I could not find much information about how they work and whether or not it will be very relevant for me.

I just simply want to produce a blend between the texture on each tile, which is all container within the same mesh. The textures are stored on a texture atlas. I have looked at the terrain and would like to produce a similar effect.

Looking at this Image you can see an example of how I would like to try and blend the ground tiles.

Any information on how to blend textures on an atlas will be very helpful. Even any alternatives would be helpful too.