simple arrangement of particles occurs in the middle of the evolution, then one can readily see that randomness increases in exactly the same way—whether one goes forwards or backwards from that point.

Yet there is still something of a mystery. For our everyday experience is full of examples in which randomness increases much as in the second half of the picture below. But we essentially never see the kind of systematic decrease in randomness that occurs in the first half.

By setting up the precise initial conditions that exist at the beginning of the whole picture it would certainly in principle be possible to get such behavior. But somehow it seems that initial conditions like these essentially never actually occur in practice.

An extended version of the picture on the facing page, in which the reversibility of the underlying cellular automaton is more clearly manifest. An initial condition is carefully constructed so that halfway through the evolution shown a simple arrangement of particles will be produced. If one starts with this arrangement, then the randomness of the system will effectively increase whether one goes forwards or backwards in time from that point.

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From Stephen Wolfram: A New Kind of Science [citation]