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And as a result, at least with respect to any of these methods all we can reasonably say is that the behavior we see seems for practical purposes random.
The resulting evolution process is likely to have attractors, potentially explaining the fact that in images such as "Magic Eye" random dot stereograms features can pop out after several seconds or minutes of scrutiny, even without any conscious effort.
Density of universal systems
One might imagine that it would be possible to make estimates of the overall density of universal systems, perhaps using arguments like those for the density of primes, or for the density of algorithmically random sequences.
Had I not been concerned with physics-like conservation laws, or had I used something other than a square grid, the teleprinter output that I generated would have shown randomization.
If the path of a crack were, say, a perfect random walk, then one might imagine that large-scale cracks could simply be combinations of many small-scale segments.
Even such individual rows seem in many respects random. … Typical vertical columns have one obvious deviation from randomness: it is twice as probable for the same colors to occur on successive steps than for opposite colors.
But although there are many seemingly random painted patterns in caves from perhaps 30,000 BC, I would be amazed if any of them were actually produced by definite simple rules.
At first an aggregation system (see page 331 ) might seem to be an obvious model for their growth: each new development gets added to the exterior of the city at a random position.
But in the third and fourth pictures, there is no such repetitive structure, and indeed the curves look in many respects random.
biological organisms are instead generated by processes whose basic rules are extremely simple—and are often chosen essentially at random.