Fractals 4 of 5: What is the shape of a cloud?

Cloud photo credits: Susan Gerofsky

 Here's a lovely thing to do together, especially on a day when the sky is blue and those fluffy cumulus clouds are moving around in the wind. Try looking up (or better yet, lying on your back in the grass) and watching the clouds.

You might try photographing or drawing them, as I've done here. But how to draw a cloud? What shape is a cloud?

We have learned the names of shapes with straight-line edges like triangles, rectangles and octagons, and curved shapes with continuous line edges like circles, ellipses and parabolas. But none of these really describes the ragged-edged (and ever-changing) shapes of clouds.

You might notice that some clouds look a lot like the maps of islands, continents and shorelines. (The bottom photo here reminds me of a map of Europe and the Mediterranean...) Shorelines are also ragged-edged and changing, more slowly, because of forces of erosion and tectonic shift. So if we can figure out what shape clouds are, we might also figure out what shape islands, continents and shorelines are!

Try looking at a small bit of a cloud you have photographed. Is there a small section of the cloud that looks almost like a miniature version of the whole cloud? If so, then you may have discovered a fractal 'seed' that can be copied bigger and bigger (and/or smaller and smaller...) to create the shape of the whole cloud! That is what is meant by a fractal: a shape that repeats itself in more or less the same way on different scales ( really tiny, small, medium, large, really large...) to create a ragged-edged and evolving shape without straight-edged boundaries.

Here is a good explanation by a meteorologist at the University of Bonn, Germany about the ways that clouds are at least partly fractals (and not always completely so, as the big central parts of clouds are not as affected by wind turbulence as the edges).

 And here is a very nice film about natural fractals, featuring the mathematician who 'discovered' fractal geometry, the late Benoît Mandelbrot!

Try drawing the shape of bumpy or ragged edge of a cloud. It might be easiest to draw it fairly large on your page. Then, on each of the 'bumps' try drawing smaller bumps that have the same shape only smaller. Do that again, three or four times. Are you getting a shape that looks a bit like the edge of a cloud -- or a shoreline?