Little can be describe from this art of photography but one hundred fold can be abstracted from such simple pictures. When it is said that little can be described it means that sometimes an abstract photograph may be simple and lacking an ornate quality, but that doesn't matter. What matters is the idea and concepts behind the photograph. What matters is seeing the picture in its truest form, void of trivial empirical forms that are solely given to most pictures of other kinds of digital photography.
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-General Definitions- -How to stop an Abstract-
-Taking Abstracts- -Selling Work-
-More Reference-
General Definitions (if there is such a thing)

Many types of photography have the applicable truth of relating ideas through images formed by conditioned facts to give us a cognitive meaning and labels. Simply put a dog picture is a picture of a dog. Through our understanding we often don't relate an understanding of what an image is by what the image means. Instead we perceive a photo as a simple label, like flower, house, insect, etc. Abstract photography looks beyond simple (what may be called) archetypes and looks for an abstract meaning out of a given photo. Just like art, the idea of a photo may be much more complex than what we see laid before us. To take and derive concepts from digital photos can be very difficult to do, because it has two layers to the formula. The layers are: taking a great looking picture, and to have a compelling concept to inspire the artist and the viewers.
How to spot an Abstract
As I said before these abstract digital photos can look (sometimes) like any other type of photos, so how do you spot a abstract photo? Abstract digital photography can have a few dead give aways (but not many). First off a lot of photographers like to shoot these types of pictures in black and white or render them in black and white later. This strips the picture of any distracting color quality, shows contrast and may give it a darker or archaic meaning. Another key factor is a lot of the pictures are shot up close or in a macro like form. A high amount of interpreting goes into deriving a idea from a macro abstract shot but they look beautiful. In nature a lot of these shots are in isolation, and will only have one signifying object to carry a pictures quality. Lastly a lot of abstract photos carry an extreme look to them or what can be called the look of 'very'.
To give an example it wouldn't be a photo of a dead tree, it would be a photo of a very dead tree. With accentuating features of one iconic motif (in this case a tree) in the photo. Other examples are: Very Rusted, Very Wilted, Very Outstanding, Very Conflicted, Very Red (or a color), etc. One thing that must be noted, the examples of 'very conflicted' and 'very outstanding' is an abstraction made from the photo, and not necessarily an objective notation of the photo itself. These descriptions are based on the relations of the object in the picture to the rest of the picture, contrarily to the other examples which may be only describing one object.
It may be a little confusing, and this isn't an exact science this is just speculative reasoning on the movement of abstract photography as a whole. You may find some totally different from your experience with the art.
Learning how to Take Abstract Digital Photos

So now (hopefully) you know what it means to take an abstract photograph, now you need to know how to take one. Let me start out by saying that every kind of photography is an art, but abstract photography has a little less of a scientific means to get to its ends. Instead every digital photo will be based on what you think is good and what you think is art. Remember art is only what you think art is, when it stops being that, it stops being art. A good way to start taking abstract digital photos is to learn the basic and then come back to the concepts. After you learn the basics here are a couple of ideas that will help you get started.

Try to find meaning where there is no abstract meaning. If you are walking through the city then try to look for photographic ideas other than simply what is laid before you. If a building says "Al's Diner" look at what abstract meaning the objects that lay before you could mean, besides a diner ran by Al. Shoot the picture at a different angle void of what people would normally associate when seeing the photo.

Use exposure in creative ways and try taking shots of things in motion at high exposure times. One person may see blurry lights you may see something different.

As was said before using black and white is a great method of creating a concept out of a photo. This doesn't mean that the black and white idea is cliche, it means it obviously works to some degree.

Go to places where nothing is found. Walking through a park can be a great way to take some beautiful pictures of trees, but not a great place to find a higher meaning. Walking through places in the middle of nowhere have a better chances of showing you things that are taken for granted.
Selling Abstract Digital Photography
If you want to start selling your abstract digital photos you can do it over a
Stock Photography Site or sell them individually over a website. The people who are buying abstract digital photos are usually using them for articles and webpages and do not really alter the state in which they are presented. There is a niche for abstract photos on stock sites and it can be profitable to invest some time selling your photos. You will keep the rights to your digital photos but they may be altered by buyers and used in ways that may not be pleasing to you. If this is the case you should sell in another means where the state of art quality will still be intact. If you do choose to sell them via stock photo sites you should know a couple of things before you do. The photo can't be something that isn't illegible and should be easily understood, so blurry photos and over exposed photos will not do (to some degree).
In order to get high sales it is all about keyword and categorization, for more information on this check out the stock photography section. Describing your photos in way so that buyers can find them is key to purchases. Try keywording your digital photos with their interpretive meaning (if easily understood). If the images obviously signify what they're intended for then people will use them as abstract images to articles in magazines and on the internet.
More Reference
To look at more work by abstract digital photographers I suggest checking out
Adam Deal. I have always enjoyed Adam Deal's work and it is a good reference point of what a good abstract photo is.