The ideas of Hofstadter and Hawkins aren't really related. Hawkins postulated a singular predictive algorithm as the explanation of how our neocortices works. Hofstadter has focused on analogies and have had some ideas similar to Hopfield networks/the Boltzmann machine. The latter fits in the trend of complex systems research, inspired as it was by spin glasses. Hofstadter worked with ideas that emerged from cybernetics, such as recursive causation and the vital role of feedback. Hawkins came from a different direction and ended up with a wholly predictive theory.
It should be noted that predictive coding predates Hawkins' work, perhaps best exemplified by Rao and Ballard's hierarchical predictive coding model from 1999. Various researchers working from similar assumptions put their thoughts together in Bayesian Brain in 2006. Since then, predictive processing has grown to be a very popular framework in neuroscience and cognitive science in general. Friston's free energy principle and philosopher Andy Clark's popularization of it have a lot to do with that.
There's been a ton of progress so far, so there's plenty of academic material for you to dive into.
It should be noted that predictive coding predates Hawkins' work, perhaps best exemplified by Rao and Ballard's hierarchical predictive coding model from 1999. Various researchers working from similar assumptions put their thoughts together in Bayesian Brain in 2006. Since then, predictive processing has grown to be a very popular framework in neuroscience and cognitive science in general. Friston's free energy principle and philosopher Andy Clark's popularization of it have a lot to do with that.
There's been a ton of progress so far, so there's plenty of academic material for you to dive into.