Conventionally, ornament has developed around linear thinking based on Euclidean geometry, and been explained as simple and lucid natural Euclidean geometrical phenomena. The modular arrangement with vertical, horizontal and diagonal grids has been an organizing principle of classical ornament, but in digital era ornament is found not to be explained only with the principle of traditional arrangement due to the seemingly irregular complex forms. In that sense, this study presents the concept of digital ornament and examined the backgrounds of ornament in digital age, that are complex system and non-Euclidean geometry. Accordingly, the present study takes an approach by dividing new formal types of ornament into algorithmic form, hybrid form and dynamic form to find out a principle of pattern organization. Lately, architects who actively use computer for their architectural designs take the algorithmic strategies in nature and create various and complex patterns by simple rules. The patterns are not the repetition of the same, but the production of singularities. In addition, hybrid form by morphing shows a topologically flexible evolutionary transformation, and is used to create in-between transitional shapes from the source to target. Finally, the patterns by the interaction between the system components which are corresponded to the embedded forces emerge from dynamic simulation of the natural environment. Rather than objects itself, focus is given to the process of generating forms, and the ornamental patterns as the revelation of such implicit order provide not just the formal beauty but also spatial pathways for lights and air, maximizing the effects of lights.