I had long been interested in map projections, so when digital geographic data became available in the 1970s, I wrote a program for producing them. A playful use of the program has been to make the map-themed annual greeting cards that are gathered here.
Most of the maps cover the whole world or a large part of it, because that's where map projections get interesting. Some demonstrate geographic facts. Some are novelties.
The capabilities of both my map-drawing program and the retail printing industry grew with time. You can see technique progress from pasted-up monochrome copy to fully electronic color composition and printing.
Only a few of the cards are shown in their entirety. Family news, free-standing greetings, and large blank areas have been elided. Card backs or parts thereof are shown only to the extent that they contain auxiliary maps or explanatory legends.
|(C*)||Conformally resurfaced globe|
|(P)||Map on polyhedron|
|1983 (CPW)||1984 (CW)||1985 (CW)||1986 (CW)|
|1987 (N)||1988 (N)||1989 (N)||1990 (H)|
|1991 (H)||1992 (G)||1993 (NP)||1994|
|1995 (CHN)||1996 (C*N)||1997 (NG)||1998 (CG)|
|1999 (CH)||2000 (CN)||2001 (G)||2002 (N)|
|2003 (P)||2004 (C)||2005 (C)||2006 (CP)|
|2007 (NG)||2008 (G)||2010 (C*)||2011 (C)|
|2012 (C*G)||2013 (CG)||2014 (CP)||2016 (CW)|
More than half the images, marked (C) in the index, involve conformal projections. You can't make a flat map without stretching various parts of the map unequally. At every interior point of a conformal projection, the stretching is simple magnification, although the degree of magnification varies from point to point. In non-conformal projections the amount of stretch varies with direction, causing shapes to be squashed or sheared.
I'm partial to conformal maps for several reasons. They are kind to shape. They have lovely mathematics (analytic functions in the complex plane). And the possibilities are boundless: The globe can be mapped conformally onto any outlined shape. This collection boasts fifteen identifiable shapes plus a movie in which the shape varies continuously from frame to frame.
I have dubbed a special family of conformal projections wallpaper maps. Repeated copies of these maps fit together smoothly to cover a flat surface, over which a journey can extend forever, with crossings of tile boundaries being as imperceptible as crossings of the the Date Line are on a journey round and round the world. There are exactly five kinds of wallpaper map; all are represented here (1983/2016, 1984, 1985, 1986, 2020). A technical report, “Wallpaper maps”, tells the mathematics of the family.
Another family consists of conformal projections onto unfolded regular polyhedra, represented here by tetrahedron (1983/2016), cube (2014), octahedron (2006) and dodecahedron (2004). There is no icosahedron in the collection; twenty faces seemed too busy for a card. The map on a tetrahedron serves also as a wallpaper map. Two cards (1993, 2003) show non-conformal maps onto polyhedra, one regular and one semiregular (with all corners alike, but not all faces).
|Azimuthal equidistant||1992||Globular (Apian)||1987|
|Dodecahedron||2004||Mercator||1990, 2002, 2011, 2013|
|Hexagon (Adams)||1986||Orange peel||1988|
|Lens||1995||Orthographic||2001, 2010, 2012|
|Pentagonal star||2005||Quincuncial (Peirce)||1984|
|Square I (Adams)||1985||Retroazimuthal (Hammer)||1994|
|Square II (Adams)||2020||Sinusoidal||1991,2008|