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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 21:20, 8 March 2009
, 21:20, 8 March 2009→Note 12: markup
Here is what I got when I just went ahead and calculated the finite differences willy-nilly:
Here is what I got when I just went ahead and calculated the finite differences willy-nilly:
{| align="center" cellpadding="8" style="text-align:center"
|-
| <math>\text{Incipit 1.}\ (u, v) = (0, 0)</math>
|-
|
<math>\begin{array}{c|cc|cc|cc|cc|cc|c}
t & u & v & du & dv & d^2 u & d^2 v & d^3 u & d^3 v & d^4 u & d^4 v & \ldots \\
\\
0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & \ldots \\
1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & \ldots \\
2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \ldots \\
3 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \ldots \\
4 & '' & '' & '' & '' & '' & '' & '' & '' & '' & '' & \ldots \\
\end{array}</math>
|-
| <math>\text{Incipit 2.}\ (u, v) = (1, 1)</math>
|-
|
<math>\begin{array}{c|cc}
t & u & v \\
\\
0 & 1 & 1 \\
1 & 1 & 1 \\
2 & '' & '' \\
\end{array}</math>
|}
<pre>
<pre>
Incipit 2. <u, v> = <1, 1>
Incipit 2. <u, v> = <1, 1>
o-----o-----o-----o-----o
o-----o-----o-----o-----o