This snowflake is an end-on view of a slightly stylised nanometre-scale gear, with the ellipses representing individual atoms.
In recent years the term has increasingly been used to describe any nanoscale products, from thin coatings to tiny particles, and any tiny objects in general.
The Nanomedicine Book Site has entire online copies of the first two volumes of work in the field, the second of which goes into detail on the potential toxicity of nanoscale compounds. The purist form of origami involves using a single square sheet of paper (white on one side, and self-coloured on the other) with no cutting or extra colouring. Koch snowflakes are an example of a fractal curve, one which exhibits a variety of unusual properties. We have a page describing the mathematics behind the Koch snowflake, as well as giving information on other fractals, which you can get to by clicking on the image opposite, or here. The hexagonal nature of the crystal arises because graphite is a form of carbon which exists as a stack of 'sheets' of carbon atoms, each sheet having a hexagonal arrangement of atoms, as shown opposite.
The crystal image was produced using differential interference contrast microscopy, a method by which differences in thickness or refractive index of a specimen can be enhanced, the colours in the image arising from interference effects.
The graphite image is used with the kind permission of Dr John Jaszczak of the Department of Physics at Michigan Technological University. The hexagonal structure in the hive is a wonderful example of the ways in which minimum-material or energy solutions tend to evolve in nature: in this case the hexagonal lattice requires the minimum of wax to surround the largest area. For some more examples of hexagonal packing in nature, have a look at the wonderful page Hexagons in a Packed World. The discovery of this structure is interesting, as it illustrates the ways in which inspiration can come from the oddest situations.

The German chemist Friedrich August Kekule, who proposed for the first time the existence of complex carbon molecular structures, also proposed a solution for the unusual properties of benzene, when it didn't at first seem to fit with the theory of long-chain carbon molecules.
When waves pass an object, they are diffracted: the path of the wave is disrupted by the object's shape (in particular the edges). The degree of diffraction is related to the size of the object and the wavelength of the incident waves. With highly complex molecules it is of course much more difficult to work out the original structure. Using various mathematical techniques, it's possible to work out the parameters of the molecule from the photograph.
The final impetus for Crick and Watson's model-building efforts came from seeing this photograph with the clearest indication yet of DNA's helical structure, and then using helical diffraction theory (much of which was due to Crick) to analyse the measurements within it. It's one of the tragedies of science that Franklin never received widespread recognition for her work.
A 'real' simulation of a nanogear assembly is shown opposite, taken from the NASA Nanotechnology Team video page, which includes many short films of running gears. Cells and other biological processes operate at the multi-atom level, and the evolution of life has involved the 'solving' of many of the problems we face when dealing with the new ways materials behave at these distance scales. Defenders point out that smaller objects are more susceptible to damage from radiation and heat (due to greater surface area-to-volume ratios): nanomachines would quickly fail when exposed to harsh climates. As the crystal grows, it adds carbon atoms to its growth faces, but in some cases, defects called screw dislocations in the crystal structure cause the atoms to be added, not in flat planes, but in a spiralling structure (a bit like adding extra steps to a spiral staircase).
The result is as if the specimen is being lit from one side (in this case from top-right), and for this image lets us see the microtopography (the tiny surface bumps :-) of the growth spiral of the crystal.

Only triangles, squares and hexagons can be used to fill a space without gaps, but for a given circumference of material, the hexagon surrounds the largest area.
There's survival merit in making the best use of available materials, so it's no surprise that there's a tendency towards the most efficient organisms. As an example, take a couple of handfuls of circular cross-section pencils and put them on a shelf between two books, so you can see the ends.
Small water waves in a tank can be visibly diffracted, while light wave diffraction starts to become obvious on the sub-millimetre scale. For example, the equal-intensity crossed pattern of dots, with empty space in the diamond-shaped regions above and below, tells us that the structure is helical (though not the number of helical chains). She died in 1958, and the Nobel Prize for Chemistry in 1963 was awarded to Crick, Watson and Franklin's colleague at King's College, Maurice Wilkins. If you shake the bundle around, it'll have an overall tendency to end up in an arrangement where the centres of the pencils form a hexagonal matrix. The vertical distance between the dots gives us the number of nucleotide units (making up the 'rungs' of the ladder) in one pitch of the helix, and the number of layers in the diamond pattern (up to the first reflection) tells you the pitch (or the repeat pattern, in this case) of the molecule. Objective risk assessment can profit from the bulk of experience with long-known microscopic materials like carbon soot or asbestos fibres. What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes.

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