### The Steepest-Descent Algorithm in Motion

The districting plan produced by the greedy algorithm is improved by a steepest-descent optimization method. Changes in color show each transfer of a county from one district to an adjacent one. A county is transferred only if the move reduces the difference in population between the donor and the recipient districts. Hence the bars of the graph move steadily toward the median population level. The algorithm stops when no further favorable moves can be found. In this case 16 transfers are made.