Disclaimer: I'm not a native speaker, so there may be some (or more) mistakes. Sorry for that.
What do I mean by "chaos theory"? And how do I think it is related to games?
Very simple answer, but as I think, probably one of the biggest wastes in the potential of video games:
I would really love to see games, that use the power of the machines we're sitting on these days. Not only in graphics, physics, sound and so on, but in the field of simulating.
In a lot of scientific fields today, they use agent-based programs, to see how certain populations behave, whether it's people reacting to economic change, or ecosystems reacting to any kind of envorimental change. The reason is that this is the best way we have today, to examine the impact of (small) changes to complex systems.
In my imagination, this could be an incredible opportunity for games. To have enviroments that actually react to the way you behave. Worlds, where your actions would have impact and not in the overly simplyfied way, that provides you with moral dilemmas, where you can be good or bad, but in a realistic way. With realistic I mean, that your actions do NOT only have the consequences you think, but - like the old butterfly and tornado metaphor - have impacts that you can not foresee.
Allright, so far so abstract.
So what kind of Game could this be? Well, I'm really not very big on technological or programming knowledge, but I think, that this kind of operation is still very demanding on processing capacity, so it probably would be asking to much, to have it implemented on a GTA-scale world.
I think it would be really cool, to have a world that behaves like that combined with limited savegames, which you could use like portaly between two worlds, that develop in different directions, depending on your actions and the actions that are provoced by those actions, but you only could have like one or two of those.
And now someone would have to come up with an actual scenario apart from that mechanic, so it could actually be a game...
The idea felt good in the beginning... kinda got stuck.
Fuck it. I post it anyway, because I still think the basic ideas are cool. Maybe somebody agrees.