What term describes an intricate design composed of flowing curves?

The term that describes an intricate design composed of flowing curves is "Arabesque." This word originates from the Arabic influence on art, particularly in Islamic design, where intricate and ornate patterns often feature interlaced floral and geometric motifs. These patterns are characterized by their complexity and the seamless transitions between curving forms, reflecting both aesthetic appeal and cultural significance.

The other options do not align with this definition. "Artless" refers to something that is natural, simple, or lacking in artifice, which does not capture the essence of intricacy and fluid design. "Apostate" denotes someone who renounces a religious belief, and "Arrant" describes something that is thorough or complete, often used in a negative context, neither of which relates to design or patterns. Thus, "Arabesque" is the clear choice for describing an ornate design made up of flowing curves.