Changes

In the current example, we already know in advance the program that generates the state transitions, and it is a rule of the following equivalent and easily derivable forms:

In the current example, we already know in advance the program that generates the state transitions, and it is a rule of the following equivalent and easily derivable forms:

2.1. F : B^2 -> B^2 such that F : <u, v> ~> <((u)(v)), ((u, v))>

| 2.1. || <math>F : \mathbb{B}^2 \to \mathbb{B}^2</math> such that <math>F : (u, v) \mapsto ( ~\underline{((}~ u ~\underline{)(}~ v ~\underline{))}~ , ~\underline{((}~ u ~,~ v ~\underline{))}~ )</math>

| 2.2. || <math>u' ~=~ \underline{((}~ u ~\underline{)(}~ v ~\underline{))}~, \quad v' ~=~ ~\underline{((}~ u ~,~ v ~\underline{))}</math>

| 2.3. || <math>u ~:=~ \underline{((}~ u ~\underline{)(}~ v ~\underline{))}~, \quad v := ~\underline{((}~ u ~,~ v ~\underline{))}</math>

2.2.  u' = ((u)(v)), v' = ((u, v))

Well, the last one is not such a fall off the log, but that is exactly the purpose for which we have been developing all of the foregoing machinations.

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:

Incipit 1.  <u, v> = <0, 0>  

Incipit 1.  <u, v> = <0, 0>  

o-----o-----o-----o-----o-----o-----o

o-----o-----o-----o-----o-----o-----o