ONT Re: Differential Analytic Turing Automata

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

DATA.  Note 5

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

For a slightly more interesting example, let's suppose that
we have a dynamic system that is known by its state space X,
and we have a boolean state variable x : X -> B.  In addition,
we are given an initial condition x = dx and a law d^2.x = (x).

The initial condition has two cases:
either x = dx = 0, or x = dx = 1.

Here is a table of the two trajectories or "orbits" that we get
by starting from each of the two permissible initial states and
staying within the constraints of the dynamic law d^2.x = (x).

d d d
0 1 2
x x x

Initial State x dx

1 1 0
0 1 1
1 0 0
1 0 0
1 0 0
" " "

Initial State (x)(dx)

0 0 1
0 1 1
1 0 0
1 0 0
1 0 0
" " "

Note that the state x (dx) (d^2.x),
that is, <x, dx, d^2.x> = <1, 0, 0>,
is a stable attractor for both orbits.

Further discussion of this example, complete with
charts and graphs, can be found at this location:

DLOG D20.  http://stderr.org/pipermail/inquiry/2003-May/000498.html

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o