Changes

==Note 5==

==Note 5==

For a slightly more interesting example, let's suppose that we have a dynamic system that is known by its state space <math>X,\!</math> and we have a boolean state variable <math>x : X \to \mathbb{B}.</math> In addition, we are given an initial condition <math>x = dx\!</math> and a law <math>d^2 x = (x).\!</math>

For a slightly more interesting example, let's suppose that

we have a dynamic system that is known by its state space X,

and we have a boolean state variable x : X -> B.  In addition,

we are given an initial condition x = dx and a law d^2.x = (x).

The initial condition has two cases:

The initial condition has two cases: either &nbsp;<math>x = dx = 0\!</math>&nbsp; or &nbsp;<math>x = dx = 1.\!</math>

either x = dx = 0, or x = dx = 1.

Here is a table of the two trajectories or "orbits" that we get

Here is a table of the two trajectories or ''orbits'' that we get by starting from each of the two permissible initial states and staying within the constraints of the dynamic law <math>d^2 x = (x).\!</math>

by starting from each of the two permissible initial states and

staying within the constraints of the dynamic law d^2.x = (x).

d d d

d d d

0 1 2

0 1 2