Draw a Hilbert curve for an 8 x 8 grid.

In a Z-curve on a 1024 x 1024 grid, the point with coordinates (0,0) is
first, the point (0,1) is second, the point (1,0) is third, and so on.
What are the coordinates of the 45th point?  Of the 57,894th point?

In a Gray curve on a 16 x 16 grid, what is the linear ordering position of a
point with coordinates (11,14)?  (Coordinate values go from 0 to 15).

Draw the "Z-curve" to cover a 8 x 4 grid.  (There is more than one possible
correct answer).  Extend you curve to a 16 x 8 grid.

Consider an 8 x 8 grid of attribute values in two dimensions.
Suppose you are given a data set with 2, 3, or 4 pages (each with equal
probability) worth of data per grid point.
Consider a one-dimensional range selection query that specifies a value of 2
for attribute A, but leaves the value of attribute B unspecified.
a. Compute I/O costs for this query, if the data is clustered row-wise
   (according to attribute A).
b. Compute I/O costs for this query, if the data is clustered column-wise.
c. Compute I/O costs for this query, if the data is clustered by a Z-curve.