An Asymmetric Sierpinski Carpet

The pattern described here was generated by an efficient recursive algorithm developed by the authors which produces approximations of self-similar fractal sets (see [3]). Such sets are constructed by a repeated scaling, translation, reflection, and/or rotation of a fixed pattern or set of patterns. The procedure is a “pattern rewriting system” in which a given geometric pattern is drawn repeatedly after suitable mappings. The pattern used to generate the fractal set by the rewriting system will be called a seed. The base is the initial configuration. The seed for this particular pattern consisted of three components. The base was a square drawn counter-clockwise. The procedure was iterated 5 times to produce the figure. Using their algorithm, the authors duplicated the self-similar fractal patterns in Mandelbrot's The Fractal Geometry of Nature [4], which constitute approximately 45% of the graphics plates in the book. This particular pattern is an original configuration…