Posts Tagged ‘zach johnson’

Per Capita Cartograms from ShowUSA

Thursday, March 5th, 2009

[Editor's note: I promoted ShowUSA's animated cartograms last week. This week I show off some of their new per capita cartograms and compare them to the raw number versions. Thanks Rick!]

CO2 emissions – per capita version
Click the interactive on the circular arrow to resize.

CO2 emissions – raw numbers version
Click the interactive on the circular arrow to resize.

Compare CO2 Emissions with Coal Fired Electric Power – raw numbers version
Click the interactive on the circular arrow to resize.

Stimulus Bill – per capita version
Click the interactive on the circular arrow to resize.

Stimulus Bill – raw numbers version
Click the interactive on the circular arrow to resize.

Early Cartograms (IndieMaps)

Monday, March 2nd, 2009

[Editor's note: Enjoy these examples of early cartograms from Zach Johnson's thesis research.]

Excerpted from IndieMaps.
Originally published there Dec. 8, 2009.

I’m kind of on a cartogram kick lately. I’m interested in the pioneers of the form, those who first thought to distort borders and explode topologies in order to convey the distribution of some thematic variable. When was the first cartogram produced, where, and by whom? I ran into a lot of material while researching my thesis; this post only begins the discussion.


The honor typically goes to Émile Levasseur for the diagrammatic maps contained in his 1868 and 1875 economic geography textbooks.

early diagrammatic map by Levasseur

H. Gray Funkhouser (1937) wrote of these “colored bar graphs”,

squares proportional to the extent of surfaces, population, budget, commerce, merchant marine of the countries of Europe, the squares being grouped about each other in such a manner as to correspond to their geographical position

Interestingly, Waldo Tobler (2004) points out that the example printed by Funkhouser (above) was sized by land area and thus not a true value-by-area cartogram. I don’t have access to Levasseur’s texts, and it’s odd that the only available scan of Levasseur’s first cartogram shows a diagrammatic map, not a true cartogram.


On the other hand is the image below, whose units are definitely sized to the data, but whose geographic arrangement is questionable. I first saw this page from an 1897 Rand McNally Atlas of the World in a SpatialCollective post; a high res version is available from the David Rumsey Map Collection.

a bubble chart, perhaps a circular cartogram, from an 1897 atlas

Circles on the left are sized proportional to population, those on the right to debt. Though the arrangement seems haphazard, geography is not ignored as the circles are grouped together by continent. I don’t really buy these as cartograms, but they’re certainly a predecessor to the circular cartogram form popularized by Danny Dorling nearly 100 years later.

Continue reading at IndieMaps . . .

E00Parser, an ActionScript 3 Parser for the Arc/Info Export Topological GIS Format (IndieMaps)

Monday, March 2nd, 2009

[Editor's note: Zach Johnson promo's his ActionScript 3 class for reading in .e00 GIS files to Flash. Useful for creating cartograms and other graphic representations reliant on topological relationships. Originally posted there Feb. 21, 2009.]

First off, why mess with such a retro format as Arc/Info Export (.e00)?– any code written for this ASCII file type in the last few years has been on how to go from e00 to pretty much anything (especially to the non-topological data format, the shapefile).

Put simply, topological information makes a lot of things possible for the intrepid ActionScripter.

Read more at IndieMaps . . .
Get the code . . .

Animated Cartograms via Show®USA and Show®World (MappingWorlds)

Thursday, February 26th, 2009

[Editor's note: These new DC-based websites display a wealth of information about the fifty U.S. states and around the world. Maps are presented both as simple choropleth (color by area) and animated non-continuous area cartograms of the type promoted by Zach Johnson over at IndieMapping. Click on the map above to see it animated to the cartogram view. Thanks Rick!

Quibbles: I wish the US map was projected into a conic like Albers and the World maps were projected, too. Some of the maps deserve a per capita view to best show their thematic data. That would be more telling than a simple cartogram. Or a cartogram that was based on per capita measure would be even better.]

Republished from SHOW®USA from
Originally published: 4 Feb. 2009.

From Spanish speakers to bales of cotton produced to number of UFO sightings, SHOW®USA ( displays each state’s numbers in animated, easy-to-understand maps that resize the state to the data rather than geographical area. The results are cartograms that bring the numbers to life–and reveal a few surprises.

“Look at our Tornado Deaths map, for instance,” says the site’s creator, Desmond Spruijt. “The most people killed last year by tornadoes were in Florida. It makes you wonder why it wasn’t in the Midwest, where our Tornadoes map shows the most storms. It turns out states like Oklahoma have better warning systems and more storm shelters, not to mention fewer people. The visual presentation makes you think about the data, to understand it better.”

Spruijt is founder of MappingWorlds, a company that helps government, non-profit, and business clients worldwide create innovative maps and cartograms. SHOW®USA is the sister site of SHOW®WORLD, which presents maps with data on the countries of the world in the same way.

SHOW®USA and SHOW®WORLD are free for public use, with no registration or personal information collected. Users can download the numbers behind the maps, which come from dozens of sources like the U.S. Census Bureau, capture and use an image of a map with animation, hyperlink to any map, and post comments about each one–all at no charge.

“To us, maps are more than pictures, they are communication and education tools,” says Spruijt. “We want people to use the SHOW®USA maps in slide shows or research papers, in the classroom–wherever our maps can make simple numbers come alive–and also to start conversations about them on our site. SHOW®USA and SHOW®WORLD also show off the kind of innovative maps we create for our clients at MappingWorlds.”

Spruijt founded MappingWorlds in Amsterdam, The Netherlands, in 2004. The company’s clients include the United Nations, the World Bank, and the International Monetary Fund.

The maps available on SHOW®USA touch on nearly every aspect of the land and people of America. Some of the current maps include: Hispanics, rural population, people with disabilities, drunk driving deaths, U.S. military deaths in Iraq, people without health insurance, strawberry production, natural gas reserves, casinos, federal farm support received, electoral college votes, food stamp recipients, gay marriages, murders, hate crimes, immigrants, charitable contributions, foreclosures, roller coasters, number of presidents born in each state, and Bigfoot sightings. With 141 maps so far, the site is still adding data and plans to have several hundred maps on display.

For those without Flash, JPG versions of the embedded SWF above:

Global Forces Converge to Drive up Oil Prices (Wash Post)

Thursday, January 8th, 2009

[Editor's note: January begins newspaper design association page contest season. We came across this graphic looking thru our 2008 work in the Washington Post and was reminded how it fits in with my geography and projections as network topology thesis. Lines on this map of "Major Global Trade Routes" of oil connect each geographic feature with related geographic features. Weights are given to each connection and represented visually. Overall the network is conformal to real geography in a top level abstract sense, but the connections (flow lines) between them shine. Kudos to Renée, now at the Wall Street Journal.]

Reprinted from The Washington Post, July 27, 2008.

In the time it takes most people to read this sentence, the world will have used up (forever) about 9,520 barrels of oil. At 40,000 gallons per second, it’s going fast.

The United States plays a central role in the global energy system as the largest consumer, the largest importer and the third-largest producer of oil in the world. With use of this finite resource rising at breakneck speed, will the world have enough to meet its needs, and will it be able to afford it?

Where does the oil come from? Just three countries — Saudi Arabia, Russia and the United States — pump about 31 percent of the world’s oil. More than 9 million barrels per day of crude oil (plus another 1 million barrels per day of liquids derived from natural gas) are being extracted from the reserves underneath Saudi Arabia, the world’s single largest oil producer.

Every day, the U.S. consumes more than 20 million barrels — almost one-fourth of all the oil used in the world and more than two times as much as the second-biggest consumer, China. Consumption in most developed countries, including Britain, France, Germany and Italy, hovers around 2 million barrels a day — barely a tenth of that used by the U.S.

Screenshots below and above. Download PDF.

Graphics reported by Brenna Maloney, graphics by Todd Lindeman — The Washington Post. Map by Renée Rigdon – The Washington Post.

Topology and Projections: 21st Century Cartography

Sunday, June 15th, 2008

maps splash walters gallery baltimore

The traveling map exhibit MAPS: FINDING OUR PLACE IN THE WORLD at the Walter’s in Baltimore, Maryland (via the Field Museum, Chicago) wrapped up last weekend. While looking at John Adam’s Road distance map of England and Wales I was put in mind of how map projections try to preserve several of:

  • Area
  • Distance
  • Shape, and
  • Direction/angle

Then the question arose: Might information (thematic) topology now be interchangable with purely geographical topology?

John Adam’s map from 1680 places towns in relative (not absolute) geographic lat-long coordinates in a rough framework that preserves their orientation to one another and in the rough-shape of their original geography. But the primary purpose of this map is to emphasize the relationship between towns and intra-town distances. Below by Royal Geographic Society.

john adams road map 1680

This topological focus (of NODES and EDGES in math-speak) is perfectly represented in Adam’s map. Circles (nodes) are inscribed with town names and straight lines (edges) connecting town circles are annotated with road distance (not straight-line geographic distance).

Modern scientific cartography, with an emphasis on visualization, might finally be loosening the geographic straight jacket to the point where purely lat-long geography doesn’t matter so much but the inter-connection (edges) of said features (nodes) gains emphases and is preserved.

I believe such thematic topology maps are “geographically” accurate and employ projection just like conventional cartography but these “projections” are as of now ad hoc and not properly defined or formalized and are often created manually. Efficient and effective mathematical formulas should be devised and listed along conventional map projections in publications like Snyder’s (USGS) Map Projections: A Working Manual.

The nearest we come to topologic maps are subway maps and cartograms. More on cartograms below.

new york subway map slice

This subway map of New York City is a topological map where the island area of Manhattan is relatively small geographically but is significantly exaggerated to accommodate the “accurate” display of the topological nodes and edges of subway stations and subway lines. (Dorling cartogram example below by Zach Johnson.)

zach johnson cartogram

Cartograms are a good example of topological maps:

  • Area of symbol represents the NODE weight alone.
  • Distance is based on EDGE weight first and and geographic distance second (trying to approximate the “relatedness” between each, eg close countries close, far countries far).
  • Direction is approximated.
  • Shape is approximated.

Zach Johnson has a good post on this topic on his blog (cartograms are the focus of his Masters Thesis).

Below a New York Times map showing the weighted electoral votes of the 48 contiguous states as the topological area of each state.

ny time cartogram example

Let us examine a map of water flow in a stream network (Kelso and Araya):

six rivers streamflow

One usually sees these maps with a conic projection to preserve equal-land-area. But the river segments are drawn exaggerated to their geographic width to represent the EDGE weight between nodes in the true geography space.

The map is dispensing with equal-land-area between nodes (the overall area and shape are preserved) and instead focusing on DISTANCE and DIRECTION between each node. The edges are “preserved” by exaggerating the stream centerlines to preserve the thematic variable. Overall SHAPE is preserved, but local land AREA is not.

Such topological maps are not diagrams because they are still rooted in land-geography; the placement of the nodes is guided by land geography but shift accordingly to best show the interrelationships between nodes. Ignoring the land-geography by listing the nodes and edges in a chart or table is not a map. A topological map takes a complex n-dimensioned space and represents that topology in a 2d dimensioned space.

precip swiss atlas

Some precipitation maps use “gridded” tightly spaced, regularized nodes and edges (above: Swiss Atlas, 2.0). The “weight” of rain and snow fall is indicated by color. Because of the spacing of the nodes and the hyper-localness of the mapped theme, this “topological map” manages to preserve both the topology and the geography.

nat geo 8th world atlas human chapter opener

The above example from the 8th Edition National Geographic Atlas of the World focuses on the quantity difference between nodes and represents that with height spikes (3d). If this were a topologic projection that needed to show the contents of each node (not the inter-relationship between nodes) the spike height would be flattened out into area alone (2.5d), leading to a grossly exaggerated land-area map but correct population-area cartogram such as:


Above from the Dutch company Mapping Worlds via Zach Johnson.

tom patterson relief example

Tom Patterson (above) uses this 2.5d term to talk about relief shading of land elevation. But I think it can be used to represent any map that is a representation of more than simply 2 variables (lat and long). Really, much of thematic cartography is 2.5d when it tries to represent complex datasets (like precipitation) with color and other visual variables.

So visualization / modern scientific cartography is focused on examining and preserving / projecting topological relationships. Often these are closely related to geographic space, but not always. That is why I am so fascinated by cartograms :)

How do we measure the “error” and “conformal”-ness in a topological map?

  • Area: Does this “view” of the topology preserve the node and edge weights?
  • Distance: Does this “view” preserve the inter-relations between nodes?
  • Direction: Both topological between nodes and geographically.
  • Shape: Purely geographical. This is what sets some cartograms above others.

For topologic shape:

Projecting a n-dimensioned topology onto a 2d surface has one or more points tangent to the 2d surface. An ideal solution shows all nodes and edges shown flattened out but this would likely require using an interrupted projection with dashed linkage lines between like-lobes content (I have seen this somewhere, need example).

For geographic shape and direction:

We are concerned with local shape (direct neighbors in the topology) and global shape. In the England example above for the Dorling cartogram the north-south direction axis tilts left in the topology. A “best” solution preserves this geographic orientation by rotating the topology network until it “conforms” more to the geography.

Finally, we can visualize this with a modified cartography cube from Zach Johnson:

cart cube zach johnson