Run the machine (by iteratively applying the transition function).

The transition from one state to another state is defined by transition functions.

It is also smooth and analytic because the transition functions have these properties as well.

The sigma points are propagated through the transition function f.

Note that the transformation law is second order in the coordinate transition functions.

Alternatively a run can be seen as a sequence of compositions of transition function with itself.

These are called the transition functions (or the coordinate transformations) of the vector bundle.

Three basic transition functions and the name of resulting models are:

At this level we do not give details of states or transition function.

The behavior of a Turing machine M is determined by its transition function.