Fractal curves that develop spatially in a linear manner over several generations give rise to captivating sculptural forms. A variety of such structures are explored using different fractal curves, with the use of multiple copies allowing the creation of closed sculptural forms that are more vase- or pot-like. More complex, visually rich, and natural forms are generated by developing fractal curves radially in three dimensions. Computer graphics, 3D printing, paper folding, and ceramic sculpture are used to explore and elaborate these constructions.