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Language: eng
Format: epub

The analogy to biology turned out to be surprisingly close. In early 1970, A. N. Zaikin and Zhabotinsky found propagating waves of excitation in thin, unstirred layers of BZ reaction. The waves resembled concentric circles, and they annihilated upon collision, just like electrical waves in neural or cardiac tissue. They even seemed to emanate from something analogous to pacemakers, randomly scattered points that belched waves spontaneously.

After learning of this work, Winfree wrote to Zhabotinsky (whom he'd met two years earlier as a fellow grad student at the Prague conference) to ask whether he'd ever seen any other wave patterns besides concentric rings. Win-free had observed spiral waves in his own lab experiments on a certain kind of fungus, but that was a far more complex system composed of living creatures with circadian clocks. He wondered if spirals could also occur in Zhabotinsky's much simpler chemical system. He doubted it on mathematical grounds; he thought he could prove that the waves had to be closed rings. But still no reply from Zhabotinsky. The mail from the Soviet Union was maddeningly slow in those days, especially between scientists (national security agencies at both ends were probably busy steaming open the envelopes). Winfree couldn't bear the suspense. He concocted Zaikin and Zhabotinsky's recipe for himself, and sure enough, spirals popped up everywhere. Winfree had no way of knowing it, but Zhabotinsky had also seen them in his 1970 thesis work, and Valentin Krinsky in Puschino had anticipated them in any excitable medium, heart muscle included. Spiral waves are now recognized to be a pervasive feature of all chemical, biological, and physical excitable media.

Boris Belousov would be pleased to see what he started.

In 1980, he, Zhabotinsky, and three other scientists were awarded the Lenin Prize, the Soviet Union's highest medal, for their pioneering work on oscillating reactions. But it wasn't much consolation—Belousov had died 10 years earlier.

The most striking thing about spiral waves is that they seem to be alive. They're self-sustaining. They don't need pacemakers: A spiral wave is its own pacemaker. If you watch one in a thin layer of excitable BZ reaction, it looks like a perpetual pinwheel, chasing its tail and regenerating itself endlessly.

In a way, the rotation is merely incidental. More fundamentally, the wave is propagating, advancing perpendicular to itself at each point along the wavefront. The confusion occurs because of a quirk about spiral geometry: Propagation looks like rotation. (Think of the optical illusion seen on old barbershop poles. The helix painted on the rotating pole seems to be propagating upward. But of course it's not moving up at all; it's merely turning along with the pole. Here rotation masquerades as propagation—the converse of the same effect in spiral waves.)

Nevertheless, there is a sense in which the rotation of a spiral wave is real. Each point in the surrounding medium oscillates periodically; it's re-excited whenever the wave passes through. So every point in the petri dish cycles through the familiar stages of excitation, refractoriness, quiescence, and then re-excitation.


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