Section 4.2 The Sierpinski gasket
A similar process can be used to construct the Sierpinski gasket, also called the Sierpinski triangle. We start with a closed, filled in equilateral triangle. The line segments joining the midpoints of the sides of this triangle divide it into four equilateral sub-triangles. We can discard the one in the center, keep the others and then repeat the process on the remaining triangles. This process is illustrated in figure Figure 4.2.1.
Many of the comments regarding the Cantor set are applicable to the Sierpinski gasket as well. It is a self-similar set consisting of \(3\) copies of itself, each scaled by the factor \(1/2.\) Its dimensional properties are, in a sense, between dimension one and dimension two.