'Creating random pixeled lines in Proccesing

I'm trying to make a game and I'm stuck on random level design. Basically, I'm trying to create a line from one edge/corner to another edge/corner while having some randomness to it.

See below image 1 [link broken] and 2 for examples. I'm doing this in processing and every attempt I've tried hasn't yielded proper results. I can get them to populate randomly but not in a line or from edge to edge. I'm trying to do this on a 16 x 16 grid by the way. Any ideas or help would be greatly appreciated thanks!

Image 2:

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randomprocessing


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