Many aspects of nature are essentially unpredictable over the long term, even when quantum effects are completely absent. A frequent cause is chaotic dynamics, which can arise when the rates of change of important dynamical variables depend in a nonlinear fashion on the variables themselves. Famous examples are the unpredictable behaviour of the weather1 and of populations of organisms2. Chaotic temporal dynamics has now been documented in practically every scientific discipline — the fascination for both scientists and the public is that chaos helps us understand what can be predicted about the systems we study, and what cannot. But our understanding of chaos in most systems found in nature, which are complex in both space and time, is relatively limited. On page 733 of this issue, Egolf et al.3 analyse the chaotic space and time variations of a heated fluid in a way that could eventually be applied to natural systems such as the weather.
The techniques of nonlinear dynamics are well developed, but its impact has been largely confined to phenomena in which there are only a few important time-dependent quantities, such as the position and velocity of a swinging pendulum. Unfortunately, this excludes a vast range of important problems in which the behaviour at one point in space can be quite different (though statistically similar) to that at another location. For example, heating a fluid from below4 — as the Earth's atmosphere is warmed by contact with the Earth — causes upwelling at some locations and descending flow elsewhere. This convective behaviour can be highly organized and predictable if the heating isn't too great, but the flow pattern becomes complex and apparently unpredictable as the heating is increased, for instance in the surface layer of the Sun. This phenomenon, frequently called 'spatio- temporal' chaos because the complex dynamics involve variations in both space and time, is the subject of Egolf et al.'s study.
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