Abstract art techniques?

Could you post any example?
There are many kind of abstractions that can be done with FF. If you show what you precisely would like to do, we can give you the right hints or suggest you a filter.

Find something such as above that you want to create then take a look through the library and find something close or something that catches your eye....Look at the filter and how its constructed then build on that to learn how things work....
ABSTRACTS

The distortions are also a good place to start in looking for methods of abstraction of an image....
Distotions

Well the only thing that I can suggest is grab some of their filters and see how they are constructed...You do not need to use the noise distortion to make distortion type of filters...
Take a look at some of mine as well I have some distortions that do not use that noise distortion component....Just like blender it does take some time to learn how things interact with each other....

btw those images above can be accomplished in Filter Forge...
Just start with some simple stuff to get used to putting together things in the editor then from there you can make other abstracts....
One thing that I do (but its just me) is when I want to create a filter that produces a certain look or abstract I will grab a reference image and use that for my background image on my desktop...This way I can stare at it when I am on my computer...
Sometimes it takes a day of staring or maybe more before I dive in to create the filter......

Here is just an example of another distortion...

Other Distortions.ffxml

mbug90 - You might check to see if Adobe Labs' Pixel Bender is still running on Windows machines. If it is, you can download a free copy of the PB toolkit here.

I used Pixel Bender for years to make abstract art, but Adobe stopped supporting PB, and then the most recent Mac OS "upgrade" (Yosemite) killed my old copy of the program once and for all. I've just started using Filter Forge in hopes of re-establishing the good workflows I had with PB.

The PB toolkit runs standalone rather than as a Photoshop plug-in -- though a plug-in used to be available for Photoshop CS5 or older. (The link for the plug-in you'll see on that page I linked to just takes you back to the toolkit page.) I don't know which filters are included in the Windows toolkit, but a very useful one was called simply, "Droste." It did a lot more than make a standard droste, though, and rendered in real time as you tweaked your image with the settings.

You can get a look at generative art I made with PB here. The starting image for many of those examples was a top-down view of a round glass vase sitting on a wood table top. Other starting images were swatch cards from the paint department at Home Depot, light coming through frosted glass, store window mannequins, and draperies hanging in a hotel lobby.

I usually broke up the starting image with Photoshop filters, most typically the Polar Coordinates or Extrude filters, and sometimes broke the images up more with various filters in PB. I'd then work with them extensively in the Droste filter and do finishing work back in Photoshop, adding texture, cleaning up any odd little artifacts, shading, edging, and so on. The finished pieces look nothing at all like the original photos.

Another option you might check out is Corel Painter, which sells for under $100. If used with a Wacom tablet and a digital brush, it mimics the process of painting with actual paint, giving you much better brush options and greater control than Photoshop. Some of Painter's automated painting features take a while to render, but just painting on your own happens in real time. You can use it with a photograph or simply paint an original image in it, but it lacks the transformative filters PB had.

Afterthought: Vladimir Golovin's Bad Trip filter has been doing some cool stuff on Day 1 of my Filter Forge life.