I've only really been taught complexity theory in relation to connectionism. And then from there it was applied to language acquisition and all sorts. There's a computer model based on it that acquires language in similar stages to that of children (Random noises -> incomplete words -> words with grammar issues like adding -ed on the end of everything -> normal sentence structure, little to no error). Complexity theory and connectionism can be pretty powerful on the theoretical level. Unfortunately it doesn't hold up when you try and find the appropriate mechanisms and responses in the brain, especially on the neuron to neruon level.
So, in linguistics I think you can get complexity theory, connectionism and pattern recognition involved fairly easily. Not sure how you would go about applying it to social anthropology. Maybe apply it and pattern recognition to the application of large scale schemata and stereotypes?