Delicate, precise and sometimes mathematical designs have long been used not only for decorative purposes, but also as a deterrent to counterfeiting on bank notes, stock certificates and other valuable documents. The intricacy of the designs is always appealing to mathematicians, and also raises the question of how they are created. In some cases, they are the result of beautifully crafted machinery; in others they are mathematically defined and executed with modern graphic software programs. Not only does this inspection lead to an appreciation of past methods and workmanship, but it also raises the question of how improved designs might be created. This paper will briefly explore thes eissues.