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But by doing Nest[s, Range[52], 26] one ends up with a simple reversal of the original deck, as in the pictures below.
But how does this sequence of digits continue?
Among all the various mathematical functions defined, say, in Mathematica it turns out that there are also a few—not traditionally common in natural science—which yield complex curves but which do not appear to have any explicit dependence on representations of individual numbers.
Systems of Limited Size and Class 2 Behavior
In the past two sections [ 2 , 3 ] we have seen two important features of class 2 systems: first, that their behavior is always eventually repetitive, and second, that they do not support any kind of long-range communication.
So just what set of structures does the code 20 cellular automaton ultimately support?
But one of the main discoveries of this book is that programs based on simple rules do not always produce simple behavior.
Needless to say, we do not have the option of explicitly setting up different initial conditions.
Instead, what they essentially do is just to take random input that comes from outside, and transfer it to whatever system one is looking at.
And so long as the boundaries of the regions do not get stuck—as happens in many one-dimensional cellular automata—the result is that whichever color was initially more common eventually takes over the whole system.
But on its own this would be quite consistent with various kinds of uniform or spiral growth, and does not imply that there will be what we usually think of as nesting.