This work presents a unified theory of vowel system typology based on a novel algorithm called Iterated Confusion Minimization, which simulates the interaction of optimal listeners and speakers over time. Compatible with existing sound change models that involve confusion-reducing adjustments to phonetic distributions, simulations over random initial vowel systems resemble observed sound change (e.g., chain shifts) and most often result in typologically dominant systems with minimal confusion, suggesting a diachronic explanation for the typological dominance of perceptually optimal vowel systems. In contrast to past vowel dispersion models, Iterated Confusion Minimization easily accounts for interior vowels like /ə/, allowing for prediction of the most common systems up to 11 vowels. Finally, variation in simulation output mirrors typological variation, with a tight correlation between system emergence rate and typological frequency up to 6 vowels that outperforms past baselines.