I'm doing a project and I need a logo to represent directory. I would like to get some feedback. Does my icon deliver the message?
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For us to perceive it as a D, you need something on the left side. It can be a line, an arrow, whatever. Your example up there looks like two arrows because that's what it is - with no other line to trick the brain. However, if something is added to the left side, the human brain automatically connects the dots and fills in the rest.
Examples of possible alternatives (quickly done up in Photoshop - merely examples and not finished products nor intended for use until fine-tuned).
As you can see, you would automatically see any of these as a D, much more so than the one you provided above. Play around with it, see what works best. Ultimately it's up to you, because as someone else mentioned, there's no need for it to look like a D unless you want it to.
A logo doesn't have to overtly represent anything. It's nice when it does, but there's no hard-and-fast rule about it.
Do I see a D by default? No. Is that a big deal? I don't know. Only you and your client can answer that.
Just a general comment...I find the weight of the arrows too light for the size and color of the box it's in. You may want to beef them up a bit. In doing that, the 'D' may become cleaer as well.
I have no problem seeing that as a D. Of course; it depends a little on the context, and it would be easier to grasp in its "habitat". @Henrik Ekblom has a good point with using it together with the name, but this is not always needed: it depends on the context you put the logo in.
If you are also asking if it is intuitively clear that it represent "directory" (I am guessing you mean directory as in telephone directory, not as computer directory?) that is a little harder. BUT, in context, it might be perfectly understandable. Never underestimate the ability for people to very quickly learn the logo and associate it appropriately. Sometimes spoonfeeding is not a good solution (a restaurant logo does not need to contain a steak, forks or checkered tablecloth).
A classic example of very elegant use of negative space, is the FedEx logo, who uses the white to create an arrow ("delivery! forward!")
There are, however, a number of ways you could make the logo a little more sophisticated, but this is of course extremely subjective. Personally, I would play making the D thicker, putting the name of the company/organisation at the bottom of the logo; maybe extending it outside the red box, using some more contrast.
Whatever you end up with; may I suggest that you pull the white D up a little. This for compensating for human visual processing: a little more air will prevent it from visually "falling down". Consider well framed artwork (there are an awfully lot of sloppy work here, curse on the mass produced!): it will have the bottom of the passepartout slightly higher than the top: