A practical problem: weather prediction
Weather (more precisely, meteorology) has played a significant role in the development of the ideas of chaos. The meteorologist Edward Lorenz was probably the first to uncover the phenomenon in numerical studies of a model of the weather; and the idea that a butterfly might unleash a hurricane has proved a wonderful headline-maker (one which the better informed are obliged to think about more deeply and critically; if you’ve reached this point, this means you!)
The problem of weather prediction provides a practical manifestation of chaos -in particular the notion of sensitivity to initial conditions and the associated horizon of predictability.
The left hand series of figures show initial conditions for a particular forecast; the differences between the patterns are small –they are a measure of the uncertainty associated with the observations on which they are based. The forecasting procedure entails feeding the initial conditions into a computer model. The right hand figures show the resulting forecasts for the weather one week later. The seemingly innocuous differences between the possible initial conditions have evolved into significantly different patterns.