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CycliST captures fundamental aspects of real-world processes by generating synthetic, richly structured video sequences featuring periodic patterns in object motion and visual attributes. CycliST employs a tiered evaluation system that progressively increases difficulty through variations in the number of cyclic objects, scene clutter, and lighting conditions, challenging state-of-the-art models on their spatio-temporal cognition. We conduct extensive experiments with current state-of-the-art VLMs, both open-source and proprietary, and reveal their limitations in generalizing to cyclical dynamics such as linear and orbital motion, as well as time-dependent changes in visual attributes like color and scale. 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