At first sight, chaos and structure seem antithetical. Yet there is an intimate connection between randomness and structure. In this talk we explain some of the ideas we have used for creative artistic design that depend on results from the study of chaotic dynamics. Our intention is to avoid the Platonistic perspective that the role of the mathematician is to dig out and discover the beauty hidden within the mathematics. Our view will be more that of an engineer. How can we use mathematics in a creative way to produce aesthetically pleasing art? (as opposed to pretty patterns.) How can we achieve the effects we want to emphasize in a particular design? We illustrate the talk with examples of (symmetric) designs, many of which have appeared in art exhibitions in the Americas and Europe. As well we give some visual demonstrations and explanations of chaos and, if there is time, indicate some practical applications of these ideas to teaching art students (some mathematics) and mathematics teachers (some art).