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Directory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
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==Note 20==
==Note 20==
In my work on "[[Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0|Differential Logic and Dynamic Systems]]", I found it useful to develop several different ways of visualizing logical transformations, indeed, I devised four distinct styles of picture for the job. Thus far in our work on the mapping <math>F : [u, v] \to [u, v],\!</math> we've been making use of what I call the ''areal view'' of the extended universe of discourse, <math>[u, v, du, dv],\!</math> but as the number of dimensions climbs beyond four, it's time to bid this genre adieu, and look for a style that can scale a little better. At any rate, before we proceed any further, let's first assemble the information that we have gathered about <math>F\!</math> from several different angles, and see if it can be fitted into a coherent picture of the transformation <math>F : (u, v) \mapsto ( ~\texttt{((u)(v))}~, ~\texttt{((u, v))}~ ).</math>
<pre>
<pre>
In our first crack at the transformation F, we simply
In our first crack at the transformation F, we simply
plotted the state transitions and applied the utterly
plotted the state transitions and applied the utterly