ONT Re: Differential Analytic Turing Automata

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DATA.  Note 11

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By way of getting our feet back on solid ground, let's crank up
our current case of a transformation of discourse, F : U% -> X%,
with concrete type [u, v] -> [x, y] or abstract type B^2 -> B^2,
and let it spin through a sufficient number of turns to see how
it goes, as viewed under the scope of what is probably its most
straightforward view, as an elsewhen map F : [u, v] -> [u', v'].

Elsewhen Map.  <u', v'>  =  <((u)(v)), ((u, v))>

u v

Incipit 1.  <u, v> = <0, 0> 

0 0
0 1
1 0
1 0
" "

Incipit 2.  <u, v> = <1, 1> 

1 1
1 1
" "

In fine, there are two basins of attraction,
the state <1, 0> and the state <1, 1>, with
the orbit <0, 0>, <0, 1>, <1, 0> leading to
the first basin and the orbit <1, 1> making
up an isolated basin.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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