Scale - Spatial Mathematics: Theory and Practice through Mapping - page 115

5.3.2 Dot density map theory
Both analysis and synthesis play important roles in mapping. We use the
dot density map to elicit validity-of-construction principles. The cartographic
example presented below displays principles of spatial synthesis as they focus
on centrality and hierarchy (Arlinghaus, 2005).
• Classical example: The dot density map employs a nested hierarchy
of regions to convert information about dots to information about
regions; in so doing, the clusters of dots emerge as centers of activity
associated with the nature of the underlying data from which the dots
were extracted.
• Contemporary example: The interactive online map may employ a
nested hierarchy that, in a single map, offers not only information of
the sort available in a dot density map but also a host of other previ-
ously impossible features, as well. It may be linked to the underlying
database in a manner that also permits:
• Scale transformation.
• Views of the database corresponding to small regions on the map.
• Searches of the underlying database.
Interactive capability can be far more than an interesting visualization tool; it
can be one offering synthesis of spatial information at a level far greater than
that available with any classical map.
A scatter of dots might represent any real world phenomenon, from the loca-
tion of emergency telephone kiosks, to small villages, to national capitals.
Dots pinpoint geographical position. At a global scale, national capitals may
appear as dots; at a local scale, they may appear as areas containing dot scat-
ter of their own. What matters is geographic scale: Dots at one scale may
not be dots at another scale. In that regard, it does not matter what the dots
represent. When the dot density map is properly constructed, it can serve as
a tool offering valuable insight into clustering.
The pattern of boundary removal, to make sense of dot scatter, is not sym-
metric. In Figure 5.3 , dots were randomized at the county level and then
viewed at the state level. Since states are larger than counties and counties
are nested within states, the opportunity to observe clusters at the state level
is optimized. If the situation exhibited in Figures 5.3 and 5.4 were reversed,
and dot scatter were randomized at the state level, and then viewed through
the county boundary lens, clear clustering errors would result.
Principle 1: Randomizing principle
In a dot density map, dot scatter is randomized at one scale and then, to
have the map make sense, must be viewed at a scale more global than
that of the randomizing layer.