How small a difference in initial conditions might be capable of causing an effect? Consider the Lorenz system, a set of nonlinear equations that govern the behavior of weather in the atmosphere. Initial conditions that must be specified in this model include the temperature, humidity, and pressure. Any particular set of initial conditions corresponds to a predicted pattern of change. Differences in initial conditions lead to unpredictability (deterministic chaos) even though the behavior is completely determined. To understand how chaos can result, suppose a description of the weather at a certain time is used, and the subsequent change in relative humidity is calculated. If the calculation is repeated exactly except for a change in the initial temperature of 0.000001° C, after a short time the system evolves along a totally different path (Figure 2).

 

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