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For k = 2 , a cell survives for s steps if these digits are all 0 (so that s IntegerExponent[n, k] ).
Repeatably random experiments
Over the years, I have asked many experimental scientists about repeatability in seemingly random data, and in almost all cases they have told me that they have never looked for such a thing.
All these parts seem to depend almost completely on detailed common conventions—and I suspect that without all sorts of human context their meaning would be essentially impossible to recognize.
In all, remarkably few messages have been sent—perhaps in part because of concerns that they might reveal us to extraterrestrial predators (see page 1191 ).
Instead, once the threshold for complex behavior has been reached, what one usually finds is that adding complexity to the underlying rules does not lead to any perceptible increase at all in the overall complexity of the behavior that is produced.
Multiplication by 2 turns out to correspond just to shifting all digits in base 2 one position to the left, so that the overall pattern produced in this case is very simple.
But it has never been at all clear just why this theory should imply that complexity is generated.
Indeed, in all the systems that we have discussed so far there is in effect always a fixed underlying geometrical structure which remains unchanged throughout the evolution of the system.
So in all of these cases the randomness one sees cannot reasonably be attributed to randomness that is introduced from the environment—either continually or through initial conditions.
But what happens if one looks not at the position of each individual particle, but rather at the overall distribution of all particles?
But in most of their obvious structural features animals do not typically look much like plants at all.