SIERPINSKI FRACTALS FROM WORDS IN HIGH DIMENSIONS

The description of fractals in two, three or higher dimensions is stra ightforward; 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 descr ibed. This construction is efficient and has a line segment representa tion which can be projected to three dimensions so that much of the st ructure of the fractal in d-dimensions can be visualized even for dime nsions higher than three.