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But as the arrangement of particles in the system becomes more random, this attempt becomes less and less successful.
And at least when there is overall apparent randomness, the networks that one gets by going forwards and backwards from a particular node will look very similar.
As the pictures at the top of the facing page demonstrate, the overall patterns produced in all cases tend to look complex, and in many respects random.
But if one looks at the fluctuations in this growth, as in the plots on the next page , then one finds that these fluctuations are in many respects random.
With an infinite random sequence of 0's and 1's, different number representations yield different distributions of sizes of numbers.
Iterated run-length encoding
Starting say with {1} consider repeatedly replacing list by (see page 1070 )
Flatten[Map[{Length[#], First[#]} &, Split[list]]]
The resulting sequences contain only the numbers 1, 2 and 3, but otherwise at first appear fairly random.
The pictures below illustrate the kind of seemingly random pattern of bubble formation that can be heard in the noise produced by boiling water.
In the mid-1860s James Clerk Maxwell then suggested that a demon operating at a microscopic level could reduce the randomness of a system such as a gas by intelligently controlling the motion of molecules.
(c) shows no obvious deviation from randomness in at least the first billion steps (after which the pattern it produces is 57,014 cells wide).
For random x , digits 0, 1, 2 appear to occur with limiting frequencies Sqrt[2 + d] - Sqrt[1 + d] .