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Although some cell types may be defined anatomically or by physiological function, a rigorous definition of cell state remains elusive. Here, we develop a quantitative, imaging-based platform for the systematic and automated classification of subcellular organization in single cells. We use this platform to quantify subcellular organization and gene expression in >30,000 individual human induced pluripotent stem cell-derived cardiomyocytes, producing a publicly available dataset that describes the population distributions of local and global sarcomere organization, mRNA abundance, and correlations between these traits. While the mRNA abundance of some phenotypically important genes correlates with subcellular organization (e.g., the beta-myosin heavy chain, MYH7), these two cellular metrics are heterogeneous and often uncorrelated, which suggests that gene expression alone is not sufficient to classify cell states. Instead, we posit that cell state should be defined by observing full distributions of quantitative, multidimensional traits in single cells that also account for space, time, and function.