The Cantor set is a mathematical object that can be constructed as follows. Start with the interval [0, 1]. The Cantor set is constructed by removing successively smaller open subintervals in an infinite process described below; what is left is called the Cantor set. First, remove the middle third of the interval. Then remove the middle third of each of the two remaining intervals; and so on. See Figure 1.

Step 0 Step 1 Step 2 Step 3 - - - . . . . Step n . . . . . . Figure 1: Constructing the Cantor set