It’s awfully bright today. The sun is too bright to look at, and when it falls on your eyes it hurts, but in an amazing happy way. The sunlight is glistening off bright white cumulus clouds, sparkling pure diamond white wherever it falls. You look up, there’s cumulus clouds everywhere like this great migrating herd through the clear cobalt sky, far, far till the horizon, and it seems like we are in this awesome photoshopped True HD movie.
Our maid observed from the balcony, looking at the clouds, that they look like cauliflower. Which is quite true of those billowy cumulus clouds.
But this similarity deserves more than a passing remark. It has got a story. Some of you know this, and I think the others will like to hear it.
Cloud surfaces are fractal shapes. A short way of explaining that is to say that as you zoom in closer to the surface of a cloud, you will see that there are curves and bulges and irregularities at smaller and smaller levels, all the way down, emerging only as you go closer in, and always looking roughly similar to the large scale curves and billows that you can see from far. So you cannot really tell how much you are zoomed in at any point. So this general irregular, non-smooth, fractured nature, together with being similar at all zoom levels, is what qualifies a shape to be a fractal.
You guessed it, cauliflower are also fractals. So is broccoli, or a bunch of other natural produce.
To try and have a grasp on the degree of irregularity or fractured-ness of a fractal, there’s this number called the fractal dimension or the Hausdorff dimension that you can calculate easily for a fractal shape. That’s not a completely accurate definition I gave, but if you’re interested, look it up. Anyway, although you cannot tell exactly what a fractal shape looks like from this number, it is still a useful way to categorize them into sufficiently narrow classes. So you can expect fractal structures with close fractal dimensions to also be visually similar.
Clouds have a fractal dimension of around 2.35. Cauliflower, around 2.28. Very close. The first fact, that their shapes have this fractal nature, is why they look similar at all. The second fact, that their fractal dimensions are close, is why they are even more similar.
This is not an isolated factoid. There’s boundless more of these if you start looking. The world is like this. As Feynman said, “Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.” These amazing little wonders are all around us. They surround us and enclose us. This is a magical world. Ask, read, know, and feel awesome.
That’s today’s sky I photographed. It was much more awesome in real life.