title: Value-by-alpha maps: An alternative technique to the cartogram.
abstract: The cartogram, or value-by-area map, is a popular technique for cartographically representing social data. Such maps visually equalize a basemap prior to mapping a social variable by adjusting the size of each enumeration unit by a second, related variable. However, to scale the basemap units according to an equalizing variable, cartograms must distort the shape and/or topology of the original geography. Such compromises reduce the effectiveness of the visualization for elemental and general map-reading tasks. Here we describe a new kind of representation, termed a value-by-alpha map, which visually equalizes the basemap by adjusting the alpha channel, rather than the size, of each enumeration unit. Although not without its own limitations, the value-by-alpha map is able to circumvent the compromise inherent to the cartogram form, perfectly equalizing the basemap while preserving both shape and topology.
authors.affiliation: GeoVISTA Center, Penn State University, 302 Walker Building, University Park, PA 16802.
authors.forename: Robert E
authors.initials: RE
authors.lastname: Roth
authors.forename: Andrew W
authors.initials: AW
authors.lastname: Woodruff
authors.forename: Zachary F
authors.initials: ZF
authors.lastname: Johnson