[source: ericjhellergallery.com]

“This image is a quasicrystal, showing some aspects of crystalline order, but missing crucial long range order we expect of a crystal. That is, with an ordinary crystal we can always move around by multiples of the repeating distances (“lattice constants”) and come to an repeated atom or structure; not so in this quasicrystal. It looks like a crystal at first glance, but then stubbornly refuses to yield to our human tendency to search for a pattern. There is no repeating pattern, not ever!”

“In Pyramid, we are looking at a small cubic sample of a perfect crystal consisting of a perfectly periodic array of three different atoms. The “projection” of a three dimensional perfect crystal onto two dimensions at some arbitrary angle, as seen here (i.e. all the atoms, which really live in three dimensions, are here drawn on the surface of the image), results in a complex pattern which has quasicrystalline aspects. A quasicrystal is something between a crystal and a random pattern; it has aspects of both; it is neither perfectly regular nor irregular.

The pattern of “obstructed” and “unobstructed” views through the crystal seen here are complex and intimately tied up with mathematical number theory.”

“Small-scale electronic devices, the size of a bacterium or even a hundred times smaller, inevitably have minute imperfections, which cause electrons to scatter and spread out as they progress through the device. We recently discovered that the electrons tend to bunch up and form branches, as is seen in many of the Transport images. In this image, the electrons are launched over a very small range of initial angles, represented by the narrow “stems”. Small initial differences in angle grow quickly, as evidenced by the fanning out and branching of electron paths. This is the beginning of the eventual chaotic motion of these electrons. Note that some branches cross. This implies that the branches are not following specific valleys in the landscape, but are subject to indirect effects caused by focusing as electrons travel over bumps and hills.

In Transport XI individual electron paths can be seen as bright lines, but if many electrons go over the same region the coloring scheme makes the image darker. “