We understand how conventional crystals grow – normal crystals assemble into large, faceted, regular-looking forms because the flat facets attract new atoms more weakly than the rougher, "uncompleted" parts of the structure, which provide more friendly neighbours for a new atom to bond with. So if you have an "incomplete" conventional crystal, it'll preferentially attract atoms to the sites needed to fill in the gaps, to produce a nice large-faceted shape that tries to maximise the size of its facets, as far as it can bearing in mind the original random initial distribution of seed crystals.
But snowflakes do something different. Their range of forms makes their growth appears pretty chaotic, but they also manage to be deeply symmetrical. It'd seem that the point of greatest attraction on a region of snowflake doesn't just depend on the atoms that are nearby, but also on the arrangement of atoms on a completely different part of the crystal, which might be some way away, and facing in a different direction, on a different spur. The sixfold symmetry of a snowflake suggests that when you add an atom to the point of one of the six spurs, the other five points become more attractive ... add an atom to the side of a spur, and we're dealing with twelve separate sites (twenty-four if the atom is off the plane). Add an atom to a side-branch, and a copy of the electrical-field image of that single atom is transmitted and reflected and multiplied and refocused at potentially tens of corresponding sites on the crystal surface. And that's for every atom in the crystal.
This would be beyond fibre-optics, and beyond conventional holography. It'd be multi-focus holography, and the holographically-controlled assembly of matter at atomic scales to match a source pattern – making multiple copies without destroying the original. It'd be using holographic projection to assemble multiple macroscopic structures that are atom-perfect copies of an original. And that idea should make the hairs on the back of your neck start to stand up.
The closest thing I've seen in print to this is the quantum mirage effect described in Nature, 3 Feb 2000. Researchers assembled an elliptical quantum corral of atoms on a substrate, and placed another atom at one of the ellipse's two focal points. They then examined the second focal point, and found that the atom's external field properties seemed to be projected and refocused at the second point, to give a partial "ghost" of the source atom [*][*][*]. You could interact with the ghost even though it wasn't there. Presumably your actions on the "ghost particle" copy would be transmitted back to the source, which'd be recreating the ghost behaviour by a process of electrical ventriloquism, using the elliptical reflecting wall to "throw" its voice to the ghost location.
Something similar may be happening in a perfectly-symmetrical monocrystalline snowflake as it grows. Maybe the crystal's regular structure just happens to not just split the image of the atom into multiples, but refocus them with phase coherence at all the key symmetry points. Maybe we could try adding a few metal atoms to one part of a snowflake crystal and seeing if matching atoms are preferentially attracted to the other corresponding sites.
A possible clue is the phenomenon of triangular-symmetry snowflakes.
It's been suggested that these form in nature when an asymmetrical snowflake falls corner-first, with the airflow disrupting regular hexagonal crystal formation (see also Wired). But since the remaining triangular symmetry is still so strong, this hints that perhaps the strongest linkage between crystal sites is in triples, with a secondary slightly weaker triplet attraction producing the hex.
Okay, so I suppose there might be problems in attempting to use giant snowflake crystals as matter-photocopiers ... for snowflake formation, every copied pattern forms an extension of the crystal, if you use the crystal to try to copy other things, then the "irregular" matter being copied is liable to disrupt of the focusing. You might only be able to copy layers an atom or two thick (at least, to start with).
But a giant atom-perfect monocrystalline snowflake would be an awfully fun thing to play with if you had a chip-fabrication lab with goodies like force-sensing tunnelling microscopes.
And to me, that was the one thing that could have justified building the International Space Station. The ability to build a giant, heavy-duty zero-gravity snowflake, hopefully one big and chunky enough to withstand eventually being brought back to Earth immersed in liquid helium for further study (what does Bose-Einstein condensate do when it's in in contact with a hex crystal?). That had to be worth a few billion in research money, and would have given the public something pretty to look at when it came time to tell them what the money had bought. We haven't done it yet, but maybe ...
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