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I hadn't thought of myself as a collector, but then I noticed how many of these I have. I still have a Michelin map of Africa from the 1970s when I worked there. Click on any of these to zoom in, but many are large files, will need good Internet bandwidth --

World Maps

It's amazing how many places you can find world maps with Mercator projection...  I'm waiting for the version done with tea leaves...
The cow sculpture is my photo; I've seen this twice now, at exhibits in Chicago USA, and Edinburgh Scotland. The next two were received in email.

Cow Maps of the World

Spilled Coffee Map of the World

and the most widely used Mercator map in the world... from Google

(this one's from 2007, it won't give directions
like these from New York to London now)

But Mercator's just one of many map projections. Here's a "map horoscope" that explains a few more of them --
Click on it two times (slowly, not double-click) to read it, or visit the original xkcd cartoon)

I first learned about Steve Waterman's "butterfly projection" from this cartoon - it not only has artistic appeal, but very high accuracy for both distances and areas. Check it out here. Waterman also wrote an educational poem about map projections, a bit kinder than the horoscope ;-)

Specialty Maps

Here's a non-geographic map - of linked datasets (see host webpage here)
Credits: Linking Open Data cloud diagram,
by Richard Cyganiak and Anja Jentzsch.

 Here's another xkcd cartoon -- linked muffins, money, vehicles, appliances, news clippings, all kinds of stuff...

Here's a rail & tunnel map built as snack trays along the train windows (Interlaken, Switzerland)

...and a tunnel map for the inside of Jungfrau peak, highest observation point in Europe. Can you name the James Bond movie that took place here?

Here's a nautical chart of the Ionian and Aegean Seas, from a sailing excursion there...

Speaking of nautical charts, here's one of the first maps
I worked on when learning about GIS -- this is an excerpt from a Digital Nautical Chart of Norfolk Virginia (1995)

This map took about 8mb in file space, but this tiny bit of data required hundreds of little files in dozens of folders. I wrote a
Smalltalk program to edit that data format, but I can't show it to you any more...

Here's where Météo-France works to make sense of the weather (2009, Toulouse) --

and one of their weather maps (for meteorologists not the public!) with insets showing vertical profiles at a point, and pressure along a path --

Ancient Maps

My most special map is the one below, that I found in an antique shop in central Texas. It's a climate map of the U.S. made around 1900 by Edwin E. Howell, US National Weather Bureau. It's about 18" high and 34" wide, painted on a plaster relief surface on a section of globe that would be 5 1/2' in diameter. The photos really don't do it justice; the detail of this map and topographic relief are exquisite. If you know anything about the history of this map, please contact me (see "Find me" page)

But that's not the oldest map I've seen. Here are some older ones -- where do you think this is?
Credits: http://www.fas.harvard.edu/~chgis/data/chgis/downloads/v4/

Andreas Cellarius rendered numerous fanciful drawings of the accepted cosmology in early 1600s, for instance these:

Plate 7. Scenography of the world’s construction according to Tycho Brahe.

Plate 24. The northern stellar hemisphere.

credits: Harmonia Macrocosmica of Andreas Cellarius

And here is a set of the oldest maps I could find easily (6200 BC to 400 AD)

Siebold, Jim; Index of Cartographic Images illustrating maps from the Ancient Period: 6,200 B.C. to 400 A.D. -- Ancient Maps, April 1998.