Future Now
The IFTF Blog
Harvard Mathematical Visualizations
As part of IFTF Tech Horizons' ongoing research on the future of mathematics, abundant computing, and lightweight infrastructure, I discovered the amazing and beautiful work of Eric J. Heller and his colleagues at Harvard University working at the intersection of physics, chemistry, mathematics and computing. Heller and his team often employ vivid visualizations as research tools to help them understand and communicate abstract phenomena like this visualization of energy moving through a nanoscale wire:
Here's how Heller describes the work:
"My digital abstract art is inspired by a world we cannot directly see; the quantum realm of electrons, atoms, and molecules. The strange, often chaotic quantum domain yields forms, which I use as a medium, creating images which convey the mystery of quantum physics.
When a water colorist puts a wet brush to paper, physics rules the result: wetting and fluid flow on paper, scattering and absorption of light by pigment on fibers, evaporation and drying hold sway. These physical phenomena mimic other aspects of the natural world and with experience can be harnessed to wonderful effect. Similar statements hold for pastels, egg tempera, oils, photographs, etc. To date, digital painting tools have tried to emulate traditional media and effects.
Digital artists need no longer emulate traditional media only! The computer allows us to create new media, with new rules, more naturally suited to the new tool. But such rules are best when they too follow physical phenomena, instead of arbitrary mathematical constructs. I have learned to paint with electrons moving over a potential landscape, quantum waves trapped between walls, chaotic dynamics, and with colliding molecules. Nature often mimics herself, and so these new media, exposing the beauty and mystery of the atomic world, yield a variety of effects that recall familiar aspects of our macroscopic experience."
There are a lot more beautiful examples on Heller's gallery page, and thorough explanations of the research on the Heller Laboratory web site of images like this:
"In this image, a quantum wave builds up in a resonant cavity between the straight and curved walls, when waves are arriving from below. Most of the wave energy is reflected back, but a surprisingly large fraction of it gets through the tiny hole if the wavelength is just right to make the cavity resonant. Prof. Robert Westervelt and his research group invented the "Westervelt resonator" around 1995 at Harvard University, for the purpose of investigating electron waves. In this picture you see various aspects of waves all acting together: reflection, diffraction, and resonance. The whole device is just a few microns across, or smaller than a bacterium."