There’s been a been a lot of ink spilled on what it is that makes Pollock’s work attractive. A paper in physics world, Fractal expressionism by Taylor, Micolich and Jonas says that it could all be about fractals. They also point out a that the idea was recently revived by Mureika, Dyer and Cupchik in Multifractional Structure in Nonrepresentational Art [PDF]. Fractals are frequently found in nature, and the attraction of the painting is that in an abstract way is describes Nature, without distracting the viewer with trees, frogs or anything else specific that might be seen in Nature.
If you prefer the forces of order to chaos then there’s also the Mondrian Generator. It’s hit ‘n’ miss at producing something interesting, but you can decide for yourself whether that suggests that Mondrian knew what made something geometrically attractive, or if he was just lucky.