When I read visual multiplication post from Hard Enough Problems, I thought that the blogger (he/she) was describing box or lattice multiplication.
I was delighted to see another take on visual multiplication. I remember to when I saw Dr. Deborah Ball for the first time about 10 years ago at a NCTM conference. I hung on every perfectly crafted word she said. I specifically remember that it was the FIRST time I had seen alternative multiplication methods in my mathematical existence. I remember Dr. Ball showing methods from other countries. As I was watching, I was furiously trying out these noveau methods on my lined paper and then double checking them with the “normal” 2 digit multiplication algorithm that I grew up with. Dr. Ball’s talk was actually about her research into the depth of mathematical understanding of teachers and how it affects the learners.
I remember being introduced to “lattice” multiplication and again being befuddled trying to learn it. I was working with a 6th grader last year who was having issues with decimal multiplication, and I showed her the lattice method. It seemed, though, that it was a little late because she (like me) had been heavily trained in the standard algorithm. Even though the algorithm wasn’t working for her because of errors of lining up numbers or carrying, lattice multiplication just didn’t feel like multiplying to her.
I guess it’s because math should be hard. always.
Reflections of a Learner 
My students love box multiplication. I do try to make sure to tell them that I hate the box method, which lets them really really love it. I have also shown them the line method. A few students use lattice, but it is too “busy” for most of my students.