You are here

Fractals—The shape of clouds

If you have noticed a young child draw clouds, you might observe that irrespective of the size of these clouds, they have the same distinctive shape. Surprisingly, there is a scientific basis for this observation and is said to be because of the ‘fractal’ or self-similar nature of clouds.

Fractals are objects that don’t have a characteristic size—they repeat themselves at all sizes. The theory of fractals is surprisingly recent. Benoit Mandelbrot published his seminal work on fractals in 1977. Since then, the fractal theory has found use in many fields, from biology (proteins show fractal behaviour in the way they fold) to the physics of fluid turbulence, and even in modern finance.

The fundamental characteristic of a fractal is its fractal dimension. The idea is straightforward. Consider a two-dimensional shape like a square, whose boundary is a ‘curve’ made up of four straight lines. Its perimeter, or the length of its boundary, is proportional to the square root of its area. However, if the sides of the two-dimensional object were fractal, the perimeter would be higher than the square root of its area. It would be proportional to the square root of the area raised to a particular power—a number we call the fractal dimension of the boundary curve.

The fractal nature of clouds was first shown in a paper by Shaun Lovejoy in 1982 published in the journal Science. The study measures the fractal dimension of the shapes that clouds of a wide range of sizes take. Using a combination of satellite and radar images, the author looked at geographical regions of sizes between 1 km and 3000 km. Areas where there is cloud-cover appear different from the clear-air regions. These areas were mapped and studied to see if the shapes that clouds take are fractal.

The study found that between 1 and 1000 km, the same fractal dimension of 1.35 is obtained, thus showing that cloud-shapes are fractal, and explaining why images of clouds are instantly recognisable, be they in children's drawings or satellite images.