There are all sorts of abstracts, if you google them you might be overwhelmed, I think.
Andy, especially for you, I collected some of my abstracts, just to show you what I consider an abstract.
(Mainly details - close ups - of bigger things, colours textures etc.
Depending on the sort of shot, I sometimes like to give the colours extra bite in post processing.
On this shot the following pictures:
Vertical pictures on the left, from top to bottom:
Drink, Paint splattered over a mural, a Drainpipe.
Right hand side, top to bottom:
Edge of a fountain basin, Corner of hotelroom furniture shot at an angle,* Victorian masonry, Detail of a wall, Detail of a shutter.
* Someone called this 3D Mondrian, which quite pleased me, especially being Dutch myself!
Hope this helps!