There are many ways to develop a creative eye, and limits for different individuals are of course different, I'll come back to this in a bit.
First, Can you answer these questions?
- What do you want to photograph?
- Why do you want to photograph it?
I think many people have different answers to these questions, and I think they (our answers to those questions) affect our photographs alot. I have wrestled with subject matter for some time, and found that my photography is altered significantly by my goals before shooting.
A simple creative exercise.
first you need an Idea.
Choose a message, or a concept. It could be important or nonsensical, some examples...
"fire requiem with butter" "Ice blue eyes" "I love the environment" "don't eat broccoli" "Photon's travel on null-space geodesics" "Love" "Hate" "Ice cream".
Let that be your goal. - let it be the answer to those above questions. "I want to photograph don't eat broccoli" "I wan't to photograph it because I want to say "Don't eat broccoli" Now you've got to solve the puzzle of how to send the message with a photograph, you'll probably end up getting creative in finding the answer.
Going back to the many ways to improve your creative eye - I believe visual language is a skill, like spoken language. Some people have more innate ability than others, learning can benefit anyone. Like a speaking and writing, if you want to be a good speaker, you should listen to many speaches and practice speaking. To be a good writer you should read many compositions and write many compositions.
When you say, "I would have never thought to take a photo of that" - you might want to look back on your goals, do they make it easier or harder for you to think in a new way? Like many of the above posters say, you should view many photographs, and take many photographs. Practice is essential, Another creative excersize is to give yourself goals, just as in learning technique, you can practice composition too. Go out, and find 6 new ways of shooting each subject you find interesting - don't allow the shots themselves to be echo's of eachother.
You don't have to have goals before you shoot, you don't have to know why you want to take photographs or what you want to take photos of, but it can certainly be helpful. It's difficult to go from being a big kid effin around with a camera, to saying something meaningful. Choosing subject matter, and what to say, I think is more difficult, than composing.
And the next time you have the thought "I wonder what it would look like from here" or "I wonder if this would work" - Don't hesitate to try it. We often don't really know until we try, and with digital, the price of film is cheap.
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A poor photographer blames his tools.