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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 17:58, 12 March 2009
, 17:58, 12 March 2009→Note 11: rearrange orbits
<math>\begin{array}{ccc}
<math>\begin{array}{ccc}
\texttt{u}' & = & \texttt{((u)(v))}
\texttt{u}' & = & \texttt{((u)(v))}
\\
\texttt{v}' & = & \texttt{((u,~v))}
\texttt{v}' & = & \texttt{((u,~v))}
\end{array}</math>
\end{array}</math>
|-
|-
| <math>\text{Incipit 1.}\ (u, v) = (0, 0)</math>
|
<math>\begin{matrix}
\text{Orbit 1}
\\
\text{Initial Point :}~ (u, v) = (1, 1)
\end{matrix}</math>
|-
|-
|
|
t & u & v \\
t & u & v \\
\\
\\
0 & 0 & 0 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 1 \\
2 & '' & '' \\
\end{array}</math>
\end{array}</math>
|-
|-
| <math>\text{Incipit 2.}\ (u, v) = (1, 1)</math>
|
<math>\begin{matrix}
\text{Orbit 2}
\\
\text{Initial Point :}~ (u, v) = (0, 0)
\end{matrix}</math>
|-
|-
|
|
t & u & v \\
t & u & v \\
\\
\\
0 & 1 & 1 \\
0 & 0 & 0 \\
1 & 1 & 1 \\
1 & 0 & 1 \\
2 & 1 & 0 \\
3 & 1 & 0 \\
4 & '' & '' \\
\end{array}</math>
\end{array}</math>
|}
|}
In the upshot there are two basins of attraction, the state <math>(1, 0)\!</math> and the state <math>(1, 1),\!</math> with the orbit <math>(0, 0), (0, 1), (1, 0)\!</math> leading to the first basin and the orbit <math>(1, 1)\!</math> making up an isolated basin.
In the upshot there are two basins of attraction, the state <math>(1, 1)\!</math> and the state <math>(1, 0),\!</math> with the orbit <math>(1, 1)\!</math> making up an isolated basin and the orbit <math>(0, 0), (0, 1), (1, 0)\!</math> leading to the basin <math>(1, 0).\!</math>
==Note 12==
==Note 12==