Sierpinski fractals from words in high dimensions

The description of fractals in two, three or higher dimensions is straightforward; however, it is difficult to effectively render the higher dimensional fractals. Construction of generalized Sierpinski fractals in d-dimensions based on a simple system of admissible words is described. This construction is efficient and has a line segment representation which can be projected to three dimensions so that much of the structure of the fractal in d-dimensions can be visualized even for dimensions higher than three.