And here is the paper covered in the original post: http://fraden.brandeis.edu/publications/papers/PNAS(2014).pd... with notes at http://www.pnas.org/content/suppl/2014/03/06/1322005111.DCSu... It's dense but not impossibly so.

One modification they made to Turing's idea was that each cell has the same composition. They found that, to produce the results they expected, they needed to alternate the composition of neighboring cells.

(It would be nice if your post was at the top of the thread, since it's the most relevant and useful so far, but it is not very controversial. Next time consider adding something like "Biology professors hate him! Read this man's 1 weird trick for explaining morphogenesis!")