Other positions for p1, p3, p3 just yield appropriately skewed gaskets. A geometric method of creating the gasket is to start with a triangle and cut out the middle piece as shown in the generator below. This results in three smaller triangles to which the process is continued. The nine resulting smaller triangles are cut in the same way, and so on, indefinitely. The gasket is perfectly self similar, an attribute of many fractal images.
Any triangular portion is an exact replica of the whole gasket.
Of particular interest is the area of the holes and the circumference of the solid pieces. As shown above the gasket has no area but the boundary is of infinite length. The gasket can also be generated a number of ways with a Lindenmayer system as illustrated by the axiom and generator below. There are many other L-Systems that can form gasket like images, one example shown below is called the Sierpinski tiling arrowhead. Figure 8 Figure 9 Sierpinski carpet Closely related to the gasket is the Sierpinski carpet.