Changes

By way of getting our feet back on solid ground, let's crank up our current case of a transformation of discourse, <math>F : U^\circ \to X^\circ,</math> with concrete type <math>[u, v] \to [x, y]</math> or abstract type <math>\mathbb{B}^2 \to \mathbb{B}^2,</math> 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 <math>F : [u, v] \to [u', v'].</math>

By way of getting our feet back on solid ground, let's crank up our current case of a transformation of discourse, <math>F : U^\circ \to X^\circ,</math> with concrete type <math>[u, v] \to [x, y]</math> or abstract type <math>\mathbb{B}^2 \to \mathbb{B}^2,</math> 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 <math>F : [u, v] \to [u', v'].</math>

<pre>

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

<math>\begin{array}{ccc}

u' & = & \underline{((}~ u ~\underline{)(}~ v ~\underline{))}

v' & = & \underline{((}~ u ~,~ v ~\underline{))}

| <math>\text{Incipit 1.}\ (u, v) = (0, 0)</math>

| <math>\text{Incipit 2.}\ (u, v) = (1, 1)</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 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.

==Note 12==

==Note 12==