We train representation models with procedural data only, and apply them on visual similarity, classification, and semantic segmentation tasks without further training by using visual memory -- an explicit database of reference image embeddings. Unlike prior work on visual memory, our approach achieves full compartmentalization with respect to all real-world images while retaining strong performance. Compared to a model trained on Places, our procedural model performs within $1\%$ on NIGHTS visual similarity, outperforms by $8\%$ and $15\%$ on CUB200 and Flowers102 fine-grained classification, and is within $10\%$ on ImageNet-1K classification. It also demonstrates strong zero-shot segmentation, achieving an $R^2$ on COCO within $10\%$ of the models trained on real data. Finally, we analyze procedural versus real data models, showing that parts of the same object have dissimilar representations in procedural models, resulting in incorrect searches in memory and explaining the remaining performance gap.