Tomorrow's weather: Cloudy, with a chance of fractals

[nebula]

Tomorrow's weather: Cloudy, with a chance of fractals

# 04 November 2009 by Robert Matthews

# Magazine issue 2733.

<snip>

The implications promise to transform the way we predict everything from tomorrow's local weather to the changing climate of the entire planet. "We may never be able to view the atmosphere and climate in the same way again," says team member Shaun Lovejoy of McGill University in Montreal, Canada. "Rather than seeing them as so complex that only equally complex numerical models can make sense of them, we're seeing a kind of scale-by-scale simplicity."

Richardson had a reputation for having ideas decades ahead of his time. He pioneered the study of fractal geometry - the study of patterns that look the same no matter how much you magnify them - though the word "fractal" had yet to be coined. Look at the honeycomb pattern in a beehive, say, and the hexagonal structure is only visible if you're not too close or too far away. But look at some kinds of plants and you'll see their fronds are made up of ever-smaller versions of the overall leaf. This is known as scale invariance, and is a feature of fractals. Richardson noticed that coastlines have a similar property, their jagged outlines appearing just as jagged as one zooms in to ever-smaller scales.

Attempting to capture this mathematically, Richardson found the same behaviour in simple formulas called power laws, by which one quantity changes according to another raised to some power. Even something as simple as tiling your bathroom wall follows a power law: reduce the length of each square tile by 1/l and you'll need l2 as many tiles. Such laws also reproduce the scale invariance of objects like ferns and coastlines, which retain the same basic form no matter how big the change in scale.

It was while looking for other examples of self-similarity that Richardson came to ponder the skies above: he noticed how the shape of clouds is constantly modified by the invisible whirls and eddies of turbulent air that surround them.

To get some insight into the laws governing turbulent fluids, Richardson performed simple experiments in which he threw bits of parsnip into a lake and watched how they moved apart under the action of the whirls and eddies on the surface. As with coastlines, Richardson found that a scale-invariant power law seemed to apply - an observation that inspired him to poetry: "Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls, and so on to viscosity" - a parody of Jonathan Swift's famous 18th-century doggerel about fleas and the little fleas that bite 'em.

But behind the humour lay Richardson's growing conviction that the atmosphere is just a collection of cascade-like processes, with large structures breaking down to feed ever-smaller ones, creating a fractal-like structure which acted according to power laws.

Full article here

[Trusting Jesus]

Fractals have always facinated me and they have always seemed as if there was more to them. Very interesting article.

<>< ><>

Nathele

[tah]

Tried to wrap this theory around my head,

but it floated away, alas, nuff said...

[traveller]

Tried to wrap this theory around my head,

but it floated away, alas, nuff said...

[nebula]

But doesn't anyone else find it interesting that so many things in nature - even clouds - are mathematically re-creatable in the form of fractals?

Can we say Designer?!

[tah]

nebula, the tile part I do not get ..sorry..over my head..

The parsnip part I get because I can see it in other things too..

thus the little rhyme...

Perhaps if you could bring it down to a 1st grade level I would get the tile part...

[nebula]

Try this website: http://math.rice.edu/~lanius/frac/

~~~

What's so hot about fractals, anyway?

They're New!

Most math you study in school is old knowledge. For example, the geometry you study about circles, squares, and triangles was organized around 300 B.C. by a man named Euclid. Much of fractal geometry, however, is much newer. Research on fractals is being carried out right now by mathematicians. Have you ever thought about a career as a mathematician?

You can understand them.

Much research in mathematics is currently being done all over the world. Most of it is extremely complicated. Although we need to study and learn more before we can understand most modern mathematics, there's a lot about fractals that we can understand.

Objects in nature often look fractal in structure.

Most objects in nature aren't formed of squares or triangles, but of more complicated geometric figures. Many natural objects - ferns, coastlines, etc. - are shaped like fractals. Here you can read about fractals in nature.

There are some really cool concepts connected to fractals.

Imagine that the picture at the top of this page is a picture of the coastline of Africa.You measure it with mile-long rulers and get a certain measurement. What if on the next day you measure it with foot-long rulers? Which measurement would give you a larger measurement. Since the coastline is jagged, you could get into the nooks and crannies better with the foot-long ruler, so it would yield a greater measurement. Now what if you measured it with an inch-long ruler? You could really get into the teeniest and tiniest of crannies there. So the measurement would be even bigger, that is if the coastline is jagged smaller than an inch. What if it were jagged at every point on the coastline? You could measure it with shorter and shorter rulers, and the measurement would get longer and longer. You could even measure it with infinitesimally short rulers, and the coastline would be infinitely long. That's fractal.

People use them to solve real-world problems.

Engineers have begun designing and constructing fractals in order to solve practical engineering problems. For example take a look at Amalgamated Research Ic.'s Fractal Control of Fluid Dynamics.

From: http://math.rice.edu/~lanius/fractals/WHY/ page

[CSLewis]

Chaos theory ?

[tah]

I have a hard time with circles and squares ... fractals look impossible ..perhaps that is why they are creating some to practice with ...

I will have to send this to my son..he has never heard of fractal math..

It will interesting to him...

[Blien]

Cool!!