BibliOdyssey has posted a stunning collection of "marbled paper designs". When I was a child, we had some old books around the house, and I remember some having patterns like this one:
This is just the one that was familiar to me. The original post has several that are much prettier than that.
The way BibliOdyssey describes the process, it sounds quite accessible to the amateur: you take a tray of water. Toss some non-water-soluble ink on the surface of the water. Throw a piece of paper on top. Take it out of the water and let it dry. The interest comes when you use multiple ink colors, surfactants to make the ink cluster into veins or avoid an area, combs or other tools to drag the ink around, move the paper while you're gradually laying it down, et cetera.
Sounds like fun. I'm tempted to try it myself. Of course, to really take it to the next level, I'd have to make my own paper.