One way to precisely define randomness is in terms of the length of the description needed to disambiguate it. A sequence of numbers, for example, can be more compactly specified if it has patterns or regularities.
A sequence is random if its description is the sequence itself. Such a sequence has no implicit patterns -- or, putting it another way, it is a pattern unto itself.
Randomness implies uniqueness, therefore, but not diversity of form, since it is devoid of patterns.
The problem is that we can never prove that no pattern exists, only that we have failed to find one. How, then, can we be certain that randomness exists at all in nature? A potentially random distribution, taken as part of a broader context, may turn out to be subsidiary to larger-scale patterns.
The tie-in to exogenous patterns within a broader context is part of what makes randomness central to the emergence of form.
Michael Webb, 2002
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