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So what does this mean for continuous models?
The procedure starts from a random configuration of squares, and then at each step picks a square at random, then reverses the color of this square whenever doing so reduces the total number of squares that violate the constraint.
But as soon as the circles have significantly different sizes, the pictures on the facing page show that this procedure tends to produce much more complicated patterns—which in the end may or may not have much to do with the constraint of densest packing.
Experience with systems from hand-held objects to engineering structures and earthquakes suggests that it can take a while for a crack to get started, but that once it does, the crack tends to move quickly and violently, usually producing a lot of noise in the process.
And in fact what I have come to believe is that many of the most obvious examples of complexity in biological systems actually have very little to do with adaptation or natural selection.
associated for example with texture and pigmentation patterns—in the end have almost nothing to do with natural selection.
And in fact there are, for example, some parts of the skeletons of animals that do seem to exhibit, at least roughly, a few levels of nesting of this kind.
And given a particular rule it turns out to be fairly straightforward to do a detailed analysis that allows one to prove or disprove its reversibility.
But it turns out that in order to do this the machine would effectively have to be able to predict where every particle would be at every step in time.
But then so, for example, do fluids like air and water.