Each axiom system given applies equally well to Nor as well as Nand .

But in many cases one can immediately tell how a sequence was made just by globally applying appropriate mathematical functions.

Spell-checking systems typically find suggested corrections by doing a succession of lookups after applying transformations based on common errors.

[Turing] machine 596440 For any list of initial colors init , it turns out that successive rows in the first t steps of the compressed evolution pattern turn out to be given by NestList[Join[{0}, Mod[1 + Rest[FoldList[Plus, 0, #]], 2], {{0}, {1, 1, 0}} 〚 Mod[Apply[Plus, #], 2] + 1] 〛 &, init, t] Inside the right-hand part of this pattern the cell values can then be obtained from an upside-down version of the rule 60 additive cellular automaton, and starting from a sequence of 1 's the picture below shows that a typical rule 60 nested pattern can be produced, at least in a limited region.

Without this additional block of black, only the first case in the rule can ever apply.

But I have little doubt that within a matter of a few decades what I have done will have led to some dramatic changes in the foundations of technology—and in our basic ability to take what the universe provides and apply it for our own human purposes.

Note that these templates apply to every cell, with templates of neighboring cells overlapping.

But for the second Results of four tries at applying an iterative procedure to find configurations which satisfy the simple constraint that every square should be the same color as the square to its right.

One may wonder, however, to what extent the behavior one sees depends on the exact scheme that one uses to pick which replacements to apply at each step.

And since one can never know in advance how far computational reducibility will go in a particular system it is always worthwhile at least to try applying the traditional methods of theoretical science.