What word best describes a design with elaborate, flowing patterns?

The word "Arabesque" is the most suitable choice for describing a design characterized by elaborate, flowing patterns. This term refers specifically to artistic designs that feature intricate, ornamental motifs often inspired by Islamic art, which includes curvilinear forms and swirling patterns. Arabesque designs are prevalent in various art forms, including architecture, textiles, and furniture, and are celebrated for their aesthetic beauty and complexity.

On the other hand, "Apogee" refers to the highest point in an orbital path, which does not relate to design or patterns. "Anodyne" describes something that alleviates pain or is soothing, which is unrelated to the visual characteristics of a design. Lastly, "Apostate" refers to someone who renounces a religious or political belief, which has no connection to the description of artistic design. Thus, "Arabesque" emerges as the clear and appropriate choice for a design that features intricate and flowing patterns.