Aperiodic tiling patterns result in endlessly varied local configurations of a limited set of basic polygons, and as such may be used to economically produce non-repeating, complex forms from a minimal set of modular elements. Several well-known tilings, such as by Penrose (2D) and Danzer (3D), have been used in architecture, but these are only two examples of an infinite set of possible tilings that can be generated by the projection in two or three dimensions of high-dimensional grids subject to rotations. This paper proposes an interface that enables the user to parametrically search for such tilings. Assembly rules are explained by which arbitrary geometry as specified by NURBS surfaces may be based on the pattern to form a non-repeating complex surface. As an  example, the fabrication in concrete of a cylindrical tiling is used to demonstrate the mass production of a continuous, free-flowing structure with the aid of a minimum amount of formwork.