Simulating SnowflakesTracy Staedter chats with David Griffeath, University of Wisconsin, who along with a colleague at the University of California - Davis, has developed a mathematical model that simulates the growth of snowflakes.
Inspecting Snowflakes When the conditions are perfect, snowflakes abound. Griffeath and his colleagues have built a mathematical model that simulates the growth of these delicate crystals.
Patterned by Nature Intricate patterns grow as they do in nature.
Mathematicians David Griffeath and Janko Gravner have developed an elaborate computer model that uses a repetitive algorithm to replicate the wildly complicated growth of snow crystals in three dimensions. It's the first time anyone has come close to demonstrating how these feathery ice crystals form in such elaborate patterns, and why. See the slide show featuring some of their snowflakes and then read the IM Interview with Griffeath below.
10:15 AM imtracynotstacy: Good morning!
griffeat: Hi Tracy. Too many google apps, too little time...
imtracynotstacy: :) I understand
Thanks for taking the time to chat this morning
griffeat: My pleasure.
10:16 AM imtracynotstacy: So the reason we're chatting is that I want to find out a little more information about your research with snowflakes.
You live in the right place for it!
10:17 AM griffeat: We had some particularly fine days for perfect crystals here in Madison this winter.
imtracynotstacy: So tell me, how long have you been studying snowflakes or ice crystals?
10:18 AM griffeat:
My work in this area is all joint with my colleague Janko Gravner at
UC-Davis. We originally started out by studying some very simple mathematical rules that grow shapes reminiscent of snowflakes. Then we started wondering how the real deals are formed. That was about four years ago.
10:19 AM imtracynotstacy: So your research area is math/algorithms?
10:20 AM griffeat:
Yes, ever since my grad student days at Cornell I have specialized in complex interacting systems with random dynamics. Snow crystals are sort of a culmination of that focus for me.
10:21 AM imtracynotstacy: I see. So why investigate mathematical rules that grow snowflake-like shapes?
10:23 AM griffeat:
Mathematicians and many physicists believe that the essential features of many phenomena in the world around us can be captured by relatively simple quantitative laws and models. Certainly the path of a ball thrown through the air that everyone studies in calculus class is a good example of that.
10:24 AM imtracynotstacy: And is there any particular reason that you were drawn to snowflakes?
10:25 AM griffeat:
I have done quite a bit of research on crystal growth. Most crystals, like quartz for instance, tend to grow with relatively simple geometric shapes. Snow crystals are fascinating because of their delicate mix of simple symmetric forms and very intricate detail and branching structure.
10:27 AM imtracynotstacy:
I read that no one has been able to accurately model snowflakes until your team did it. Is that right? If so, why are snowflakes so difficult to model?
10:30 AM griffeat:
People have been trying to understand the essential features of snow crystal evolution since Kepler and Descartes in the 1600s. Many of the physical principles have just become clear in the past few decades. But incorporating those principles into a feasible computer algorithm has just now become practical. It does seem we are the first to get the basic three-dimensional features right. The delicate balance of physical forces at play makes this enterprise very challenging.
10:31 AM imtracynotstacy: When you say "basic 3-D features," what are you referring to? Can you give me an example?
10:34 AM griffeat:
Well, for instance, in the familiar stellar dendrites that most folks think of as typical, of course the snowflake is not really two-dimensional -- it is about 100 times as wide as it is thick. Along
the middles of the six arms are characteristic "ridges" that our model reproduces even though we had no ability to build them in. The model builds them on its own.
10:36 AM imtracynotstacy:
Hmm. So what does the model do exactly? Does it start with a basic 3D feature, such as the stellar dendrite, and then build a snowflake from that? How does it work?
10:41 AM griffeat:
It tries to mimic the physics. The model starts with a small seed you
can think of as a few pixels within a 3-D video array. Over and again for hundreds of thousands of updates, external "particles" of virtual vapor diffuse until they reach the boundary of the crystal and then decide whether or not to attach (freeze) depending on local geometry and the parameters of the model. Once the crystal is many millions of times as big as when it started we have a virtual snowflake. In our model each chunk that sticks actually represents a little prism of ice about a micron on a side.
10:42 AM imtracynotstacy:
Wow that's really cool. So is it true that no two snowflakes are alike
in nature? And if so, does that ring true in your model?
10:44 AM griffeat:
Yes, a question we get all the time. Alas, if you think about it, this
question makes very little sense since it's not at all clear what
"alike" means. There is absolutely no chance that two crystals will be identical at the molecular level. With a crude enough perspective lots of them are very much alike -- especially the simple hexagonal prisms that are plentiful under certain conditions. The whole question is just one big grey area.
10:45 AM imtracynotstacy: So where is this research going from here? What do you do next?
10:48 AM griffeat:
For starters we would really like to optimize our code so instead of taken an entire day to get one specimen (with no knowledge in advance whether it will be a "good" one), we can maybe cut that down to an hour or so. Then the really big problem is to try to connect the attachment parameters of our model to the underlying physical parameters like temperature, saturation, and pressure. That remains very very challenging, but we hope our model provides some clues. There are also potential applications to meteorology and nanotechnology we hope to explore.
10:49 AM imtracynotstacy: Could you say more about those potential applications? What might they be?
10:52 AM griffeat:
The weather application would be for remote sensing (from space via
satellite) to try to measure precipitation levels in remote regions of
the earth. The amount of water reaching the ground during a snowfall
depends dramatically on the shape of the crystals that are falling.
Having good digital approximations for the many snowflake morphologies
should help interpret the signals obtained actively and passively by
the satellites.
10:53 AM The
nanotechnology goal would be to understand more about molecular self
assembly and what local organizing principles might give rise to very
small materials with desired patterns, designs, etc.
10:55 AM imtracynotstacy: I see. So let me ask you this: When it's snowing outside, do you pay more attention than non-snowflake-modeling people?
10:56 AM griffeat:
I have come to learn what weather patterns are likely to make for good
snow crystal watching. On such days I pay lots of attention. But
usually, in our blizzards, say, I just shovel and head back indoors.
10:57 AM imtracynotstacy: Ha! So what makes a good snow crystal, by the way?
11:00 AM griffeat:
The temperature should be pretty cold -- around 0F - 10F for good
dendrites. The cloud cover should be low and the air should be still so
that individual crystals fall gently without bumping each other. It's
even nice to have a little sun so the flakes glitter as they gently
fall. On such a day the beautiful ones will fall in droves on your
parka or car windshield. Good places include the Great Lakes region,
Vermont, Ontario, and Hokkaido.
11:02 AM imtracynotstacy:
Well, it's bordering on spring, so we may not have too many days like
that left. But it's good to know that those cold ones produce some
beautiful items.
11:03 AM griffeat: There's always next year!
imtracynotstacy: Yes. Well, thanks so much taking the time to chat about your work in this area. It's been fun.
11:04 AM griffeat:
And I hope folks will check out some of the movies of our model. They
really give a good idea how these marvels get to be the way they are.
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