There are a million things that Twitter is great for: finding a lunch recommendation, finding a hairdresser, finding a lost pet. But just plain finding a user, or a business? Tough. Although Twitter’s search is decidedly better than it was, say, a year and a half ago – particularly if you take the time to use the parameters in the (buried within Twitter) Advanced Search – it’s definitely not worth writing home about.

You can argue, of course, that Twitter wasn’t designed for that purpose: shouldn’t you be using the power of the social grid itself in place of a search engine? And while that’s not entirely true, it’s also a valid point that most of us don’t make the most of Twitter’s interconnectivity. Apart from occasionally tracing the trail of someone’s retweet and following a person or two as a result, the average Twitter user isn’t necessarily interested in – or able to – invest the time in mining the information available from his followers, or those followers’ followers, or … well, it could go on forever.

With that in mind, here are a few fun toys for better visualizing the Twitter hive mind. Like it or not, we’re better equipped to navigate huge amounts of interconnected info when we’ve got a representation laid out in images, not just text. Have favorites of your own? Drop us a line in the comments and let us know. Enjoy!

Mentionmap. View an ID or a hashtag by connections it makes to other users or hashtags, then refocus and repeat. While there are a lot of tools that do similar, this one’s clear, clean and speedy. (We’ve seeded our example with our own Twitter handle, @WorldCoSocial. Can you connect your own ID with us using Mentionmap?)

Twitterfountain. Throw it a keyword and watch the tweets roll past. It’s not really a sophisticated piece of kit at all – for example, you can’t click on an individual tweet to load it and start off on another tangent – but it’s strangely mesmerizing, particularly for watching updates on a frequently-mentioned topic like, say, this weekend’s homecoming game. Plus, you can customize background images based on Twitter keywords.

Twitter Friends Network Browser. A similar starburst-map visualizer to Mentionmap, but limited to user names. The fun thing about this one is the ability to click on one of your followers, expand their follower starburst, then play a little six-degrees-of-separation in order to try to get back to yourself again.