Dynamics of space
Space can be modeled in different levels of complexity depending on the properties one would like to retain and
depending on the predefined purpose. Let's look at the following example to illustrate the complexity: the ambler who
moves
in space. A plane and homogeneous surface is the simplest perception of space. The ambler can move in every direction
with
the same comfort. The distance to his destination would be a function of the Euclidian distance, measured from his starting
point. His path would connect the starting point and the destination point by a straight line, giving the distance. In
this
case, the space is described as a plane and isotropic surface. Space is supposed to be a
homogeneous, isotropic surface and the distance is calculated based on the coordinates. But we have to be aware that
such a
surface without obstacles and without elements determining spatial dynamics does not exist in reality.
Imagine the ambler moving on a plane but heterogeneous surface with different land use types, vegetation covers, different
geological formations etc. The observer will realize that the ambler's path is influenced by friction elements. The space
is
differentiated by specific properties, thus heterogeneous. This surface is still supposed to be isotropic.
This means that the properties don't change with direction. But in this context, the Euclidean distance is not adequate
anymore
for the calculation of the distances. Other measurement units are necessary such as time or energy needed to go from
one point
to another based on the concept of weighted distances. To account for the surface's heterogeneity,
the geometric aspects of the entities, which compose the space, have to be considered as well as their properties. Forests
and
marshland influence the movement differently.
Consider the ambler moving in a rough terrain. In addition to the changing land cover types there is the topography as
an
element of friction taken into account. The topography acts as a gravitational force, depending on the slope, influencing
the
ambler's approach and certainly his path. The orientation of the movement is connected to the gravitational force. This
space can
be seen as anisotropic surface. It allows to include the area of influence of other phenomena
which affect the ambler, e.g. wind and all other exterior forces influencing direction or orientation.