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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 16:00, 28 February 2009
, 16:00, 28 February 2009→Note 5: markup
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 <math>d^2 x = (x).\!</math>
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 <math>d^2 x = (x).\!</math>
{| cellpadding="8" width="100%"
{| align="center" cellpadding="8" style="text-align:center"
| <math>\text{Initial State}\ x \cdot dx</math>
| width="90%" |
|-
|
<math>\begin{array}{cccc}
t & d^0 x & d^1 x & d^2 x \\
t & d^0 x & d^1 x & d^2 x \\
\\
0 & 1 & 1 & 0 \\
0 & 1 & 1 & 0 \\
1 & 0 & 1 & 1 \\
1 & 0 & 1 & 1 \\
|}
|}
{| align="center" cellpadding="8" width="90%"
<br>
|+ <math>\text{Initial State}\ (x) \cdot (dx)</math>
| align="center" |
{| align="center" cellpadding="8" style="text-align:center"
| <math>\text{Initial State}\ (x) \cdot (dx)</math>
|-
|
<math>\begin{array}{cccc}
<math>\begin{array}{cccc}
t & d^0 x & d^1 x & d^2 x \\
t & d^0 x & d^1 x & d^2 x \\
\\
0 & 0 & 0 & 1 \\
0 & 0 & 0 & 1 \\
1 & 0 & 1 & 1 \\
1 & 0 & 1 & 1 \\
<pre>
<pre>
Note that the state x (dx) (d^2.x),
Note that the state x (dx) (d^2.x),
that is, <x, dx, d^2.x> = <1, 0, 0>,
that is, <x, dx, d^2.x> = <1, 0, 0>,