Panorama of Fractals and Their Uses

Rivers

The area-perimeter relation can be applied to rivers, if
Ai is the area of the basin drained by the river,
and
Pi is the length of the longest branch of the river.
both measured at length ri, then we expect P2/P1 = (A2/A1)d/2.
Measurements of this sort were made by Hack.
Choosing a reference length r1 and plotting
Log(A1/Ai) versus Log(P1/Pi)
gave points approximately on a straight line of slope d/2= 0.6, thus d = 1.2 for rivers in the eastern US. A similar analysis for rivers in the western US gave d = 1.4.

Return to Rivers.