Abstract photographs are something I have been doing for years. I love me a an abstract photograph me, where that is on the streets, in the woods, at the sea side, anywhere. I love something that makes you think or just makes you appreciate how different the subject matter is within an abstract composition.
There are several different elements that go into an abstract composition, which includes very similar decisions to other photography e.g. colour to B&W, macro/ close up, focal length, lens, etc. These are important, but for tend to be secondary. Allow me to elaborate. Not only am I pretty much a run and gun video maker, a lot of my photography is done on the fly. I will grab whatever equipment is around me an just go out and shoot, or just happen to have a camera on me when I am out and about, and decide to take some photographs.
For me the subject is key. Is it a uniform pattern that needs something extra to add that abstract element? Is it a disgusting piece of fungus or natural part of nature that has grown in an unusual way? A lot of nature has fantastic patterns and colours within it, and chaos is king. There is also opportunities for abstracts within man made towns and cities. Concrete metropolises and metal constructs offer up unique chances for more abstract compositions. Reflections and water can also pay a part in this. I would suggest playing around with wet windows or mirrors.
In fact, along with water and reflections, focus can play a large part. Soft focus or back focusing can be just or more effective that pin sharp focus. Indeed, this can add to the feel of the photograph. Think about playing around with the depth of field, and how this interacts with the way you are focusing the lens. Manual focus is extremely useful when considering an abstract composition.
Lens choice is less important for me, but can be very important if you are putting together an composition with an idea in mind. If you know the results you want to achieve, have a think about the focal length that would compliment this. For me, I tend to use whatever camera/ lens combination I have on me at the time.
Lastly, but not least importantly is post processing. Black & white or colour? Does the white balance need to be more obscure to compliment or highlight specific parts of the photograph? Did you try cropping at different ratios to see what will work? Does more emphasis need to be made on the subject, perhaps a vignette? All of these elements work towards being the icing on the cake. However, they will not make a bad picture a good one.
At the end of the day, the hard work must be done in frame with the camera and lens. Once you have a good useable photograph, you can them flavour it as needed to compliment the base ingredients. Start thinking about playing with forms and shapes, different angles (golden angle, Fibonacci spiral). Keep it simple. even within a chaotic image, there is simplicity. Sometimes this can be what makes the photograph really shine. Look for simplistic chaos and uniform obscurity. Break the rule of thirds unless it helps build a better composition.
Most of all, practice your abstracts as much as possible, the more you try, the more you will be able to see with your photographers eye. - Sly.