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Even simply-defined, finite-state generators produce stochastic processesthat require tracking an uncountable infinity of probabilistic features foroptimal prediction. For processes generated by hidden Markov chains theconsequences are dramatic. Their predictive models are genericallyinfinite-state. And, until recently, one could determine neither theirintrinsic randomness nor structural complexity. The prequel, though, introducedmethods to accurately calculate the Shannon entropy rate (randomness) and toconstructively determine their minimal (though, infinite) set of predictivefeatures. Leveraging this, we address the complementary challenge ofdetermining how structured hidden Markov processes are by calculating theirstatistical complexity dimension -- the information dimension of the minimalset of predictive features. This tracks the divergence rate of the minimalmemory resources required to optimally predict a broad class of truly complexprocesses.

Divergent Predictive States: The Statistical Complexity Dimension of Stationary, Ergodic Hidden Markov Processes