Adjacency patterns:  one viewpoint.  The dot density map. It is interesting to consider how to use a GIS to do some analysis of mapped information--using a bit of creative effort. Dot density maps:  layer of randomization, layer of observation--scale change; absolute representation (1 dot represents 1000 people) and relative representation (1 dot represents 0.1% of the population of the state).  Use ArcView. The concept of clustering is tied to scale. Equal Area Projections and dot density maps--one way to look for clustering in geographic space. Select a distribution that can usefully be represented as dot scatter--such as population. Then, choose polygonal nets of at least two different scales--such as state and county boundaries. Let the map with the smallest spatial units (counties) be used as the randomizing layer--the dot scatter is spread around randomly within each unit. View the scatter through polygons (states) that are larger than are those of the randomizing layer (counties).  Map 1 shows the results of removing the county boundaries; Map 2 shows the national picture with state boundaries; and, Map 3 views the dot scatter through the national border lens.  The clustering of dots at the state level means something; at the county level it is merely random. Select an equal area projection (such as an Albers Equal Area Conic for the U.S.). Because the underlying projection is an equal area projection, a unit square (or other polygon) may be placed anywhere on the map and comparisons made between one location and another.  Indeed, urban or rural measures might be held up to a value associated with similar polygon tossed out randomly. Interesting reading on related topics:  Mark Monmonier and Harm deBlij, How to Lie with Maps, University of Chicago Press.