Timeline for Shape of snowflakes
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Apr 1, 2017 at 17:36 | comment | added | Daniel Litt | @Olga: I haven't thought about this in many years -- it's rather far outside my wheelhouse. If you have any specific questions, I can try to dig up the old code, though... | |
| Apr 1, 2017 at 17:32 | comment | added | Olga | Are there some news/explanations for the "hexagonal"model you tried here? | |
| S Aug 17, 2015 at 18:58 | history | suggested | Ilmari Karonen | CC BY-SA 3.0 |
reupload images from imageshack to stack.imgur before they get replaced by ads; see http://meta.stackexchange.com/q/263771
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| Aug 17, 2015 at 18:52 | review | Suggested edits | |||
| S Aug 17, 2015 at 18:58 | |||||
| Mar 14, 2012 at 20:00 | comment | added | j.c. | Your random models don't quite capture the character of the processes that make snowflakes spiky because in diffusion-limited aggregation type models (those related to snowflake growth), the growth rate at boundary sites is not uniform, but rather is the harmonic measure from infinity, which is more heavily weighted on "spiky" regions of the boundary. | |
| Mar 14, 2012 at 13:52 | comment | added | Benoît Kloeckner | The random model looks very close to the Richardson growth process; my web page shows 3D images www-fourier.ujf-grenoble.fr/~bkloeckn/images.html and Olivier Garet's one has many images of related random processes iecn.u-nancy.fr/~garet/images.php | |
| Dec 26, 2011 at 1:19 | comment | added | user6976 | @Daniel: I know some people who know these subjects. I will ask when I see them. | |
| Dec 25, 2011 at 19:15 | comment | added | Daniel Litt | @Mark: I have no idea, unfortunately; I don't know much about either subject. | |
| Dec 25, 2011 at 19:14 | history | edited | Daniel Litt | CC BY-SA 3.0 |
added 1029 characters in body
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| Dec 24, 2011 at 23:50 | comment | added | user6976 | Nice! Is it similar to percolation clusters, self-avoiding random walks, etc.? | |
| Dec 24, 2011 at 23:19 | comment | added | Daniel Litt | (And indeed, my simulations suggest the shape properties are essentially the same as the ones given here for $p$ close to $0$ or $1$.) | |
| Dec 24, 2011 at 23:19 | comment | added | Daniel Litt | I think I can show that your objection doesn't effect the "shape" properties I'm discussing here (e.g. in points 1-5), only the growth rate. But if you have some "shape" property in mind that you can show differs in the model you suggest, I'd be happy to hear it. | |
| Dec 24, 2011 at 23:13 | comment | added | Rebecca Bellovin | It's not the same as assuming no molecules attach at the same time, because in your random model you're effectively adjusting the probability of attachment based on the size of the snowflake. If anything, you want to adjust the probabilities based on the geometry --- I would guess that available vertices deep "inside" the snowflake would have lower probabilities of attachment. | |
| Dec 24, 2011 at 23:07 | comment | added | Daniel Litt | @Rebecca: In fact, I just coded up your suggestion--unsurprisingly, it seems to interpolate between the two models here (very similar to the first if $p$ is large, and similar to the second if $p$ is small). | |
| Dec 24, 2011 at 23:01 | comment | added | Daniel Litt | This is really just the same as assuming no two molecules attach at exactly the same time, which happens with probability $1$ anyway in any continuous model... | |
| Dec 24, 2011 at 22:58 | comment | added | Rebecca Bellovin | I don't like your random model: it seems much more reasonable to fix a probability p and at time t, attach a new hexagon at every available lattice point with probability p. Assuming a fair amount of water in the air, water crystallizing at one vertex should be independent of water crystallizing at other vertices (to a first approximation). | |
| Dec 24, 2011 at 22:47 | comment | added | Daniel Litt | I'd be happy to send the Processing code/java applet to anyone who'd like to play with these models--my email is in my MO profile. | |
| Dec 24, 2011 at 22:31 | history | answered | Daniel Litt | CC BY-SA 3.0 |