Chapter 7.2, Problem 29MS

Cantor Squared. Draw the four corners of a square, label them 1, 2, 3, 4, and start at one corner. Randomly choose a number from 1 to 4. Move 2/3 of the way to the corner whose number comes up from wherever you are at the time. Repeat forever. Verify that, with this process, any point in the Cantor Square will move to another point in the Cantor Square. Notice that, as you continue the process, the points will approximate the whole Cantor Square.