Are there any good / interesting analogs to regular expressions in 2d?

Question

Are there any good (or at least interesting but flawed) analogs to regular expressions in two dimensions?

In one dimension I can write something like /aaac?(bc)*b?

Answer 1

Not being a regex expert, but finding the problem interesting, I looked around and found this interesting blog entry. Especially the syntax used there for defining the 2D regex looks appealing. The paper linked there might tell you more than me.

Update from comment: Here is the link to the primary author's page where you can download the linked paper "Two-dimensional languages": http://www.mat.uniroma2.it/~giammarr/Research/pubbl.html