ONT Re: Differential Analytic Turing Automata

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DATA.  Note 7

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Here are the 4^th gear curves over the 1-feature universe
X = <|x|> arranged in the form of tabular arrays, listing
the extended state vectors <x, dx, d^2.x, d^3.x, d^4.x>
as they occur in one cyclic period of each orbit.

d d d d d
0 1 2 3 4
x x x x x

Orbit 1

0 0 0 0 1
0 0 0 1 1
0 0 1 0 1
0 1 1 1 1
1 0 0 0 1
1 0 0 1 1
1 0 1 0 1
1 1 1 1 1

Orbit 2

1 1 0 0 1
0 1 0 1 1
1 1 1 0 1
0 0 1 1 1
0 1 0 0 1
1 1 0 1 1
0 1 1 0 1
1 0 1 1 1

In this arrangement, the temporal ordering of states
can be reckoned by a kind of "parallel round-up rule".
Specifically, if <a_k, a_(k+1)> is any pair of adjacent
digits in a state vector <a_0, a_1, ..., a_n>, then the
value of a_k in the next state is (a_k)' = a_k + a_(k+1),
the addition being taken mod 2, of course.

A more complete discussion of this arrangement is given here:

DLOG D24.  http://stderr.org/pipermail/inquiry/2003-May/000503.html

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