Lab 5: Iterated Function Systems: The Sierpinski Gasket
On a piece of graph paper shade a 32 x 32 box square. This square is stage 0.
For stage 1, take another sheet of graph paper and shade three 16 x 16 unit squares, as if you divided the original shaded square into four equal squares and then excluded the upper right corner.
For stage 2, take another sheet of graph paper and shade nine 8 x 8 squares, as if you subdivided the three shaded squares from the previous stage and then excluded the upper right corners of each shaded shaded square. Notice the unshaded square that appears in the center.
For each successive stage, continue as we have described above. Replace each shaded square from the previous stage as if you had subdivided the square into for equal squares and then excluded the upper right corner.
If you continue this process indefinitely, you will construct the Sierpinski Gasket. Can you express the number of squares that you shade at each stage as an exponential expression? What stage would you have to reach in order to shade at least one million squares? Your assignment is to draw the construction to stage 5.
