- A few years ago, during a visit to the University of Toronto, I was
able to try out last week's BZ reaction recipe myself. Ray Kapral and the
good folks there set me up with a lab coat, protective goggles, Petri
dish, pipette, and all the necessary ingredients. Aside from sucking too
hard at one point, thereby ingesting a bit of Ferroin, the cooking went
flawlessly. Sure enough, some sweet little spirals developed. To see
counterparts of my computer experiments arise in the 'real world' of a
chemistry lab was truly inspirational.
- That said, there are so many advantages to computer simulation of nonlinear
physical dynamics that even applied types are increasingly drawn to
virtual reality. Toronto's
Michael Menzinger sums it up thus:
- For instance, the
CoLoS Project at Oxford University uses both workstation- and Web-
based interactive visualization to study a wide assortment of problems in
physical and theoretical chemistry. Here is a snapshot of
target patterns generated by their BZ simulation tool.
- This week's soup, produced by our WinCA
software, shows a Greenberg-Hastings (GH) rule after 100 updates started from a
completely random configuration of 8 colors. Though we offered several GH models
during the first few months the Kitchen was open (see Recipes 2,
4, 14, 17),
we have not yet featured parameters that illustrate prototypical nucleation
of spiral pairs (ram's horns) in excitable media. The neighborhood here is range 3
Box, with a threshold of 5 excited neighbors needed to activate a resting cell. The palette
depicts excitation as a fire ranging from fully excited = orange, through successively darker
shades of red for the refractory period, to black for resting (excitable). By the time shown
this process invariably locks into a locally periodic state in which every cell cycles with
period 8.
- GH dynamics are simple enough that they are rather surprisingly amenable
to rigorous mathematical analysis. On the downside, they lack some of the
subtler physical features of the actual BZ reaction and related excitable
media. For this reason many applied researchers implement more complicated
computer algorithms, with additional parameters, either to better fit
empirical data or to capture additional detail. Perhaps the best known
variant is the Hodgepodge Machine of Gerhardt and Schuster, popularized in
a Scientific American article by A. K. Dewdney in the late 1980's. There is a page
of CA graphics from a Parallel Computation Group in Madrid that features a striking
2d Hodgepodge type image. Computers have also been used, by Arthur
Winfree and others, to study the analogs of ram's horns in three dimensions: scroll rings
and more intricate topological structures.
Jörg Heitkötter offers a rather nice 3d Hodgepodge graphic.
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