Oddly...I love this idea of letting things lie where they fall. Interesting. This is definitely a project one wouldn't attempt in a rental though.

In a rental, or for extra durability, you could spill paint or actual liquid latex on a sheet of canvas and then cut along the edge of the puddle to create a similar looking throw rug.

hey AMLitt great idea, i am going to do that for my sons room! we are renting so cant spill real paint! yikes!