Some background information: This first got started because I tweeted an image at @pixelsorter and @badpng (see the thread here: https://twitter.com/wayspurrchen/status/514246071464521728/p..., I wrote a blog post here: http://wayspurrchen.com/blog/2014/09/the-eternal-robot-love-...), which spawned a really interesting infinite loop. Eventually, the other bot's creator reset her bot and that infinite loop ended, but people caught wind of it and have been making my bot enter infinite loops with other image bots ever since.
I think @a_quilt_bot and @pixelsorter are a particularly interesting pairing though, because @a_quilt_bot can generate new sources of imagery that my bot can further resort, resulting in a neverending stream of new, automatically generated imagery. My bot is also rate-limited by the Twitter API (350 API calls per hour), so there's no technical reason my bot and another rate-limited bot couldn't keep communicating forever. I'm actually really interested in this idea, and it's the center concept behind my next project idea.
I wonder if you could build some kind of distributed neural net on top of twitter or another social network. Find some way to get nodes with very little computation power hidden within a free app, webpage, screensaver or something, and use twitter as a communications channel instead of IRC or whatever. The social graph stuff is already built in.
Twitter seems to be terrible at detecting and banning bots - I wonder how fault-tolerant something like this would have to be. After all, the bots would be following generally good heuristics of communicating with one another, albeit probably not in natural language. They would probably have insane login patterns, however.
 Or a botnet, if you're feeling evil.
Presumably if you sustain that level of tweeting for awhile they'd warn you or suspend your account.
It's a deliberate attempt by High Frequency Tweeters to manipulate the tweetosophere! In fact, Twitter is so one sided in it's tweeting patterns that genuine twits have given up responding to the communication of other humans and merely tweet based on tweet stuffing interventions by those who plead innocence and claim to only be providing useful information.