In this paper, the potential to generate a wide range of designs using an algorithm that creates Menger-type fractal constructions is explored. The authors describe a method that can be used to build a Menger-type figure from which, the initial “atoms”, the rules and distances can be changed to create many interesting figures. Furthermore, this method can be applied in a new variation called Menger-Diaz. The Menger-Diaz variation is created by modifying the way the atoms are placed, not removed, at each level, resulting in a shape with unique properties and characteristics that are demonstrated through several examples. Therefore, this method can lead to applications of these designs in artistic works.