Some people don't like or 'get' abstracts. I love them!
I like form, pattern and texture as a composition in it's own right, and I don't think a photograph needs to be recognisably 'of' something. I also don't think that an abstract or pattern always needs a focal point- indeed having one may destroy the overall feel of the picture and become the subject rather than the pattern or texture itself.
I particularly like photographing details and abstract patterns in nature- I find these more beautiful than anything man can create. The wonderful details of nature captured by Ansell Adams were one of my first and strongest influences in photography as a teenager, and I still find these more compelling than many of his big landscapes.
The skill is in spotting a simple and effective composition amongst the surrounding complexity, trying to really convey the beauty you can see and feel. It is much harder than it looks! It really makes you look more closely at your environment, and tune into it. In a good location I can spend literally hours in tiny area- best done alone!