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Revision as of 02:20, 2 March 2009
, 02:20, 2 March 2009→Note 7: markup
==Note 7==
==Note 7==
Here are the <math>4^\text{th}\!</math> gear curves over the 1-feature universe <math>X = \langle x \rangle</math> arranged in the form of tabular arrays, listing the extended state vectors <math>(x, dx, d^2 x, d^3 x, d^4 x)\!</math> as they occur in one cyclic period of each orbit.
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
{| align="center" cellpadding="8" style="text-align:center"
0 1 2 3 4
| <math>\text{Orbit 1}\!</math>
|-
|
<math>\begin{array}{c|ccccc}
t & d^0 x & d^1 x & d^2 x & d^3 x & d^4 \\
\\
0 & 0 & 0 & 0 & 0 & 1 \\
1 & 0 & 0 & 0 & 1 & 1 \\
2 & 0 & 0 & 1 & 0 & 1 \\
3 & 0 & 1 & 1 & 1 & 1 \\
4 & 1 & 0 & 0 & 0 & 1 \\
5 & 1 & 0 & 0 & 1 & 1 \\
6 & 1 & 0 & 1 & 0 & 1 \\
7 & 1 & 1 & 1 & 1 & 1 \\
\end{array}</math></p>
|}
<br>
{| align="center" cellpadding="8" style="text-align:center"
| <math>\text{Orbit 2}\!</math>
|-
|
<math>\begin{array}{c|ccccc}
t & d^0 x & d^1 x & d^2 x & d^3 x & d^4 \\
\\
0 & 1 & 1 & 0 & 0 & 1 \\
1 & 0 & 1 & 0 & 1 & 1 \\
2 & 1 & 1 & 1 & 0 & 1 \\
3 & 0 & 0 & 1 & 1 & 1 \\
1 1 0 0 1
4 & 0 & 1 & 0 & 0 & 1 \\
0 1 0 1 1
5 & 1 & 1 & 0 & 1 & 1 \\
1 1 1 0 1
6 & 0 & 1 & 1 & 0 & 1 \\
0 0 1 1 1
7 & 1 & 0 & 1 & 1 & 1 \\
0 1 0 0 1
\end{array}</math></p>
1 1 0 1 1
|}
0 1 1 0 1
1 0 1 1 1
<pre>
In this arrangement, the temporal ordering of states
In this arrangement, the temporal ordering of states
can be reckoned by a kind of "parallel round-up rule".
can be reckoned by a kind of "parallel round-up rule".
