And as another way to use this idea - when you do randomly find something to photograph - before hitting the shutter take a moment to think about what that 'something' means to you, what is it that caught your eye. The clearer you have that in mind, the clearer your photograph of it will probably be.
Here's a great idea to help you flex your creative muscles for photography.
To really push the artistic side of your photography - choose a random word from the dictionary, a book on your coffee table, or from a 'word of the day page' (ie http://www.wordthink.com/). Really study that word and what it means.
Then go for a walk with your camera. When something catches your eye, spend a few moments thinking about that word - and then take some pictures of whatever has caught your eye.
The two may be totally unrelated things - but then that's what art often is, taking an object, scene, colour etc and adding meaning beyond the literal.
The more you do this, the more you should be able to add a different kind of depth to your photography.
Most of all, have fun with the idea.