You decide to color a square that measures \(1 \mathrm{~m}\) on each side in a very particular manner. You first cut the square in half vertically. You color one side of the square with purple. On the side of the square that was not colored, you draw a line dividing that region horizontally exactly in half. You color the lower half blue. Now, you cut the remaining quarter of the square precisely in half with a vertical line. You color the left side red. You repeat this process 12 times. After you color that 12th piece, what is the total area you have colored?