Working on a logo

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Well, I’m working on a logo for the design of my website (http://www.dujodu.com - nothing to look at right now though, just a placeholder) And I drew it out on paper and decided I should make the basic shape in illustrator, since it seemed logical. I’ve never used illustrator before really, but as I expected it was simple enough for something as… simple… as this. So now I have a basic shape and want any suggestions/comments before I take it any further. If this looks insanely similar to another logo, please tell me! It’s a big version on the left, and a small version on the right. And on a side note… is there a way to snap to grid in illustrator? I have it showing grids, and “snap to point” is turned out, but it seemed like it either wasnt working (maybe snap to point isnt what i need?) or I had to be pretty exactly on the intersection for it to snap.