Distortions of image structure can go unnoticed in the visual periphery, and objects can be harder to identify (crowding). Is it possible to create equivalence classes of images that discard and distort image structure but appear the same as the original images? Here we use deep convolutional neural networks (CNNs) to study peripheral representations that are texture-like, in that summary statistics within some pooling region are preserved but local position is lost. Building on our previous work generating textures by matching CNN responses, we first show that while CNN textures are difficult to discriminate from many natural textures, they fail to match the