Introduction

    We enter into this discussion already in possession of some intuitive appreciation of periodicity, having observed with curious fascination waves surging onto a beach, a full Moon dominating the night sky once each month, the determined arcs of a child on a swing, the clockwork sway of a pendulum, or similar periodic phenomena.  Indeed, we are each intimately familiar with circadian rhythms, our internal timepiece regulating our daily activities.  From this, undoubtedly, much of our appreciation and delight for periodicity stems.

    While other disciplines of science explored the periodic -- physicists with their pendulums, biologists with circadian rhythms, and mathematicians with sinusoidal waves -- chemistry, until recently, was bereft of this study.  Although there had long been evidence that the rate of some reactions changed repeatedly, many chemistry luminaries thought it would be contrary to the Second Law of Thermodynamics for a chemical reaction to oscillate.  However, applying the concepts equilibrium thermodynamics to non-equilibrium systems proved erroneous.  Yet this thinking so held the day that when Boris P. Belousov, director of the Institute of Biophysics in the Soviet Union, submitted a paper to a scientific journal purporting to have discovered an oscillating chemical reaction in 1951, it was roundly rejected with a critical note from the editor that it was clearly impossible.  His confidence in its impossibility was such that even though the paper was accompanied by the relatively simple procedure for performing the reaction, he could not be trouble.  Arthur C. Clarke best captured this spirit of this folly with Clarke's First Law: "When a distinguished but elderly scientist states that something is possible he is almost certainly right. When he states that something is impossible, he is very probably wrong."

    Belousov had been attempting to model the Krebs cycle, when, purely by accident, he observed that a solution of citric acid, acidified bromate (BrO₃^-), and a ceric salt oscillated periodically between yellow and clear.  However, due to aforementioned resistance among the chemistry community to chemical oscillators, the published work did not appear for several years; even then, appearing only in the proceeding of an obscure medical conference.

    The dropped flag, fortunately, was taken up some years later by another Russian biophysicist, Anatol M. Zhabotinsky.  Zhabotinsky refined the reaction, replacing citric acid with malonic acid and discovering that when a thin, homogenous layer of the solution is left undisturbed, fascinating geometric patterns such as concentric circles and Archemedian spirals propagate across the medium.  Therefore, the reaction oscillates both in space and time, a so-called spatio-temporal oscillator.  Despite initial frustration at the resistance of journal editors, who knew this to be quite impossible, Zhabotinsky was ultimately able to prevail and publish several papers concerning what would become known as the Belousov-Zhabotinsky Reaction (or the BZ Reaction, for brevity's sake).  The evidence was undeniable: chemical reactions could oscillate, demonstrating periodicity.