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To be honest, I have never thought of trying

To be honest, I have never thought of trying to hack the problem in such a brute-force way until just now, and so I know enough to expect a not unappreciable probability of error about all that I've taken the risk to write out here, but let me forge ahead and see what I can see.

to hack the problem in such a brute-force way

until just now, and so I know enough to expect

a not unappreciable probability of error about

all that I've taken the risk to write out here,

but let me forge ahead and see what I can see.

What we are looking for is -- one rule to rule them all,

What we are looking for is — one rule to rule them all, a rule that applies to every state and works every time.

a rule that applies to every state and works every time.

What we see at first sight in the tables above are patterns

What we see at first sight in the tables above are patterns of differential features that attach to the states in each orbit of the dynamics.  Looked at locally to these orbits, the isolated fixed point at <math>(1, 1)\!</math> is no problem, as the rule <math>du = dv = 0\!</math> describes it pithily enough.  When it comes to the other orbit, the first thing that comes to mind is to write out the law <math>du = v,\ dv = ~\underline{(}~ u ~\underline{)}~.</math>

of differential features that attach to the states in each

orbit of the dynamics.  Looked at locally to these orbits,

the isolated fixed point at <1, 1> is no problem, as the

rule du = dv = 0 describes it pithily enough.  When it

comes to the other orbit, the first thing that comes

to mind is to write out the law du = v, dv = (u).

 

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==Note 13==

==Note 13==