Assigned Exercise V.2. Let Bo be the filled unit square (box of side length 1) in the plane. Construct a fractal by dividing Bo into 16 just touching boxes each of side length 1/4 by dividing the sides of Bo in 4 segments of equal length. Then remove from Bo the 4 boxes in the center, leaving a generator B consisting of a perimeter of 12 boxes of side length 1/4 (the center was hollowed out). Let A be the fractal obtained by repeating the same hollowing process on each of the small boxes remaining in B, and continuing indefinitely, calling the n-th stage of construction B. (a) Show by induction that the area of the n-th stage of construction, B., is ". (b) Determine the box counting dimension of A. Is it the same as the similarity dimension of A? Show your work. (c) Find the Hausdorff distance between B, and B2. Show your work with a picture. What then is the Hausdorff distance between B, and Bs (no picture required, but explain anyway)? Assigned Exercise V.2. Let Bo be the filled unit square (box of side length 1) in the plane. Construct a fractal by dividing Bo into 16 just touching boxes each of side length 1/4 by dividing the sides of Bo in 4 segments of equal length. Then remove from Bo the 4 boxes in the center, leaving a generator B consisting of a perimeter of 12 boxes of side length 1/4 (the center was hollowed out). Let A be the fractal obtained by repeating the same hollowing process on each of the small boxes remaining in B, and continuing indefinitely, calling the n-th stage of construction B. (a) Show by induction that the area of the n-th stage of construction, B., is ". (b) Determine the box counting dimension of A. Is it the same as the similarity dimension of A? Show your work. (c) Find the Hausdorff distance between B, and B2. Show your work with a picture. What then is the Hausdorff distance between B, and Bs (no picture required, but explain anyway)