One of the simplest ways to represent a trajectory 
is by direct spatial encoding of the time dimension; then the
trajectory can be read sequentially from the fixed field.
(This process is like playing an audio tape.)
More precisely, suppose 
is a time-varying field
defined over an extent 
(that is, 
), and we
want to generate it over the relative time interval 
.
Let 
be a mapping from the
time interval to another domain of spatial extension; then
the trajectory 
is encoded by a fixed field
over 
defined by:
[ [u, h(t)] = _u(t) . ]
The field 
is ``read out'' by sweeping v from
h(0) to h(T).
Since the area of the field 
is proportional to the
duration of the signal 
, such a representation is
feasible only for signals that are comparatively smooth with
respect to their duration.
(Specifically, by the Nyquist theorem,
there must be as least two representational
units v per unit time for the highest frequency component
of 
.)