It is a reality that non objective art has been popular in the New York art scene for many years (some time after WWII). I can't say exactly where it stands today. It is a-kin to such movements as color fields, futurist or cubic abstraction, but non objective art is a mode with marked differences in artistic interpretation. Its strongest aspect the absence of original subject. In other words non objective art does not resemble any real world object nor should it be inspired by one.
Here non objective art made with computer graphics resembles the real thing quite closely. Of course it takes away the craft of making the painting, which might put an even further gap between the human element and viewer. I have heard many people say that modern art, like this, feels cold. I can't say that I disagree. I will say that this strongly design oriented hard edge work has a strength of it own in pure color and direct movement. Non objective painting follows arts tradition, and our preference, for harmonious colors and balanced composition.
If you see some non-objective art, and many contemporary museums have some of it, I suggest that you try not to think what it means, but about it's relationship to art in the broader sense. This type of painting can be very successful in capturing a feeling or a concept which words do not impart.
also see Rudolf Bauer