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But now what the cellular automata do is to take specifications of positions of cells, and then in effect compute directly from these the colors of cells.
But knowing how to do this requires having behavior that is in a sense simple enough that one can foresee every aspect of it.
To what extent does what one sees capture the features of mathematics?
Do they typically force the operator to have a particular form, or not?
And the point is that if computational irreducibility is present, then there is in a sense all sorts of information about the behavior of a system that can only be found from its rules by doing an irreducibly large amount of computational work.
For as we have seen, many systems that just occur in nature actually end up doing more computation than typical systems that we explicitly set up for a purpose.
It is suspected but not established that there exist at least some problems in NP that cannot be solved in polynomial time, potentially indicating that for an appropriate system it might be impossible to do cryptanalysis in any time polynomial in n .
Our visual system does not immediately perceive the grids, but instead mainly picks up features formed from local arrangements of dots.
Up to limited m nested sequences can contain all k m possible blocks, and can do so with asymptotically equal frequencies.
And even today some Western superstitions center on animism, as do rituals in countries like Japan.