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People use Twitter for lots of different purposes. I use Twitter to keep up with friends, find new things on the 'Net that I wouldn't otherwise see, and to tell others what I'm thinking. Another word for that final purpose is "influence." To a certain extent almost everyone on Twitter is trying to use it to influence something--some more blatantly than others.
If you've been on Twitter for any time you'll notice that people have different behaviors with respect to their avatars. Some put them up and never change them. Some put up their own face. Others put up pictures of their family, logos, or even book covers or favorite brands. Some people change their avatars frequently and some have had the same avatar since they set up their account.
As an aside, when you pick an avatar, something recognizable is nice, but not necessary--I'll pattern match eventually even if I can't tell what it is. Also, one of my pet peeves is people who use pictures that are looking to their own left. Most Twitter clients put the picture on the left of the text and the picture ought to look at the text, not off to the side. If you're using a face, pick pictures that are facing to their right and make the face big enough to be recognizable.
I understand the desire to use the avatar in Twitter for personal expression. But if influence is part of your motive for using Twitter, then changing your avatar frequently is a bad idea. Here's why.
One measure of influence on Twitter is the number of followers. To refine that we might use an algorithm that determines who your followers are and their influence--kind of like Google page rank, but for tweeple. Certainly there are sites that do that sort of thing. But the ultimate measure of influence is how often your tweets are read. No way to measure that, as far as I know. But there is a way to increase the probability: pick an avatar you like and stick with it.
I subscribe to almost 700 people on Twitter. That means that my Tweetstream is in constant motion with new stuff on it all the time. As i scan it, your avatar is one of the clues I use to determine whether to read a particular tweet or not. I read every tweet that some people make; others I read only occassionaly. My primary clue is the avatar. More than once I've missed people because they decided to express themselves and change their avatar.
Obviously you can change your avatar if you like. But if you're trying to express yourself, leave your avatar alone and write a well thought out 140 characters. That will get across much more forcefully than anything else you can do and the probability I'll see it and read it will go up because you'll be familiar to me as I scan the tweetstream.