Abstracto

Relationship between area and perimeter

Kathryn Sandals

Following Mandelbrot's fractal theory, the area-perimeter relation is utilized to investigate the geometry of cloud and rain areas measured by satellite and radar between me and 1.2 x 1 square kilometer. The results corresponded to a formula in which the perimeter is roughly equal to the square root of the area raised to the power D (P VKD), where D is the perimeter's fractal dimension. The perimeters of rain and clouds are discovered to be fractals with no obvious horizontal length scale between 1 and 1000 kilometers.