Numerous methods have been proposed to transform color and grayscale images to their single bit-per-pixel binary counterparts. Commonly, the goal is to enhance specific attributes of the original image to make it more amenable for analysis. However, when the resulting binarized image is intended for human viewing, aesthetics must also be considered. Binarization techniques, such as half-toning, stippling, and hatching, have been widely used for modeling the original image's intensity profile. We present an automated method to transform an image to a set of binary textures that represent not only the intensities, but also the colors of the original. The foundation of our method is information preservation: creating a set of textures that allows for the reconstruction of the original image's colors solely from the binarized representation. We present techniques to ensure that the textures created are not visually distracting, preserve the intensity profile of the images, and are natural in that they map sets of colors that are perceptually similar to patterns that are similar. The approach uses deep-neural networks and is entirely self-supervised; no examples of good vs. bad binarizations are required. The system yields aesthetically pleasing binary images when tested on a variety of image sources.