It is often reported that people like objects that are in order, predictable, or can be processed fluently. We suggested that we do not enjoy simple order as much as the process of ordering and therefore we like images that allow for insight— even in perceptually challenging contexts. Furthermore, perceptual challenge together with a promise of perceptual ordering could trigger interest. We report two studies which utilized patterns produced with different intentions (to be liked or interesting, etc.) by rotating visual elements via the software Flextiles. Participants evaluated the patterns on various dimensions regarding the potential for order-detection and perceptual challenge. Liking was predictable by potential for order-detection but not by complexity. Meanwhile, interest was predictable by a moderate potential for order-detection together with high complexity. Furthermore, patterns intended to be interesting were associated with perceptual challenge: less obvious order, more flaws of order, and more time to decide whether the image contains an order. Study 2 additionally included patterns intended to be beautiful or ugly, as well as random patterns. Liking was again predictable by potential for order-detection. Interest, in contrast, was predictable by a combination of potential for order-detection and high complexity. Complexity alone was not a significant predictor of interest this time, whereas patterns intended to be interesting were more perceptually challenging than those intended to be liked or beautiful. Our findings indicate that liking might be related to the potential for ordering, but interest requires association with order but also perceptual challenge.