generation: 0points: 1

The Hilbert curve begins at generation zero as a single point in the middle of the square. Subsequent generations are formed by a recursive process of replication and linking. Four shrunken copies of the curve are distributed to the four quadrants of the square, then reoriented so that the end of the curve in one quadrant lines up with the beginning of the curve in the next quadrant. To achieve this alignment the southwest quadrant has to be rotated a quarter turn clockwise. The southeast quadrant rotates a quarter turn counter-clockwise and then flips across the horizontal axis. (These two transformations are equaivalent to a reflection across the major diagonal.) Finally, line segments are drawn to joint the four quadrants into a single curve.