Changes

==Note 3==

==Note 3==

I will draw on those previously advertised resources of notation and theory as needed, but right now I sense the need for some concrete examples.

I will draw on those previously advertized resources

of notation and theory as needed, but right now

I sense the need for some concrete examples.

Let's say we have a system that is known by the name of

Let's say we have a system that is known by the name of its state space <math>X\!</math> and we have a boolean state variable <math>x : X \to \mathbb{B},</math> where <math>\mathbb{B} = \{ 0, 1 \}.</math>

its state space X and we have a boolean state variable

x : X -> B, where B = {0, 1}.

We observe X for a while, relative to a discrete time frame,

We observe <math>X\!</math> for a while, relative to a discrete time frame, and we write down the following sequence of values for <math>x.\!</math>

and we write down the following sequence of values for x.

x

t & x \\

"Aha!" we say, and think we see the way of things, writing down the rule <math>x' = (x),\!</math> where <math>x'\!</math> is the state that comes next after <math>x,\!</math> and <math>(x)\!</math> is the negation of <math>x\!</math> in boolean logic.

 

"Aha!" we say, and think we see the way of things,

writing down the rule x' = (x), where x' is the

state that comes next after x, and (x) is the

negation of x in boolean logic.

Another way to detect patterns is to write out a table

Another way to detect patterns is to write out a table

of finite differences. `For this example, we would get:

of finite differences. `For this example, we would get: