We present color sails, a discrete-continuous color gamut representation that extends the color gradient analogy to three dimensions and allows interactive control of the color blending behavior. Our representation models a wide variety of color distributions in a compact manner, and lends itself to applications such as color exploration for graphic design, illustration and similar fields. We propose a Neural Network that can fit a color sail to any image. Then, the user can adjust color sail parameters to change the base colors, their blending behavior and the number of colors, exploring a wide range of options for the original design. In addition, we propose a Deep Learning model that learns to automatically segment an image into color-compatible alpha masks, each equipped with its own color sail. This allows targeted color exploration by either editing their corresponding color sails or using standard software packages. Our model is trained on a custom diverse dataset of art and design. We provide both quantitative evaluations, and a user study, demonstrating the effectiveness of color sail interaction. Interactive demos are available at www.colorsails.com.