The Ebstorfer mappamundi, map of the Christian World in the 13th century overlaid with an image of Christ. (click for high resolution)

The Ebstorf mappamundi was drawn in 13th century Saxony and depicts the Christian worldview within the body of a crucified Christ. The map illustrates both the “known world” as well as significant landmarks and points of interest for the curious pilgrim.

Christ’s head is in the East, at the top of the map, the direction of Paradise. His hands mark the northern and southern limits of the known world, and his feet are at Gibraltar where the Mediterranean meets the Atlantic. In the middle of the map we see Jerusalem, the spiritual center of Christendom, located at Christ’s navel. Europe is in the bottom left quadrant of the map, Africa in the bottom right, and Asia dominates the upper half.

In the East, near Christ’s head, is the Garden of Eden surrounded by mountains. Just west are the Chinese (note the two figures bent to gather silk) and the Indians. In the Indus Valley we see opium eaters, people who stare at the sun all day (gymnosophists), as well as that strange tribe who subsists only on the scent of apples. Alexander the Great is consulting the Oracle of the Sun and the Moon.

Details from the Ebstorfer Mappamundi. Left: Places in India, including Alexander the Great consulting the Oracle, the Opium Eaters in their poppy field, and a gymnosophist staring at the sun. Right: Mt. Sinai (oriented sideways), and Sodom and Gommorah covered by the Dead Sea.

At the center of the map, near the all-important Jersulaem, we can find the Tower of Babel, Bethlehem (marked with the Star of David), Sodom and Gomorrah, and Mt. Sinai.

Africa and northern Asia both are hinterlands illustrated with mythical creatures and legends. In Africa, a tribe of dwarfs rides crocodiles. In Asia, two Amazonian women guard their citadel.

Maps such as this may explain much of the surprise 15th and 16th century explorers felt as they sailed to the Americas and around the Cape of Good Hope. Africa was much bigger than this map indicates, and the invisible Americas were very much in the way of a direct sea route to India. We know that the ancient Greeks had discovered that the world was round, and circa 1400 AD Ptolemy had produced an accurate map of Europe and Asia based on a spherical Earth. But the Ebstorf map follows the Roman tradition of placing landmarks in relative positions, maintaining basic order and structure but not following rules for measurements or Cartesian accuracy. And the T-O structure of this map—the base of the T was the Mediterranean, the cross was at Jersualem; the O formed the surrounding oceans—was an idealized depiction of the world that was all too common in the late medieval era.

Despite its shortcomings as a navigational aid, the Ebstorf mappamundi is a beautiful map. It is both a sacred object glorifying the Body of Christ and also a tourist map of the strange and wonderful places that formed the background of medieval storytelling.

References:

• Art and Cartography by David Woodward
• The Ebstorf Mappamundi by J. Siebold

Markets are People, published 1930 by Printer's Ink

“Markets are People” is a beautifully drawn map. It uses area-distortion to show population at both the state and city level. This is the first map we have seen that uses the area-distortion method at two resolutions. The effect is visually accurate, highly readable, and offers deeper insight into the data than similar maps that offer only one level of detail. (For comparison, look at modern cartograms on Wikipedia.)

Notice how easy it is, for example, to estimate the percentage of urban population in any given state: Illinois is about 50% urban. Relative sizes of cities are also easy to estimate.

This map was found in Graphic Presentation, published in 1939 by Willard C. Brinton, p. 242. The caption under the map reads:

Printer’s Ink Publishing Co., Inc. Chart by Walter P. Burns and Associates, Inc. New York City.

A Distorted Map of the United States Showing Population of Each State and Cities of 50,000 or More in 1930.

The presentation of cities whose areas are proportional to their population is the outstanding feature of this map.

The entirety of Graphic Presentation is worth exploring. It covers a full range of topics from color theory to line graphs and “quantitative cartoons”. The book is out of print, but we found a wonderful leather-bound copy at the university library. A PDF of the full text is also available.

Thanks to Datavisualization.ch and Flowing Data for pointing us to this book.

London trains and metro map, 1874

Jonathan Stott’s thesis Automatic Layout of Metro Maps Using Multicriteria Optimisation (PDF) is a comprehensive look at the state-of-the-art of automatic transit map generation. The premise: start with a geographic map of subway or transit stations and lines, then convert this map into an abstract yet informative representation of the transit system akin to those standard transit maps found in the world’s major cities. My aim in this post will be to provide a brief summary of Stott’s thesis.

Aesthetics of the transit map

Transit maps have existed for centuries. From their genesis, these maps have expressed a tendency towards simplicity—perhaps encouraging customers to visions of quick and simple travel in an age when trains and ferries were still novelties and their complexity not yet understood. The 1874 London trains map removes much of the city clutter for the sake of a simple, almost playful, representation of rail lines and stations (see above).

But the classic example in this space is Harry Beck’s 1933 map of the London Underground. Previous maps of the London Underground had maintained high geographic accuracy for line and terminal position. Beck’s landmark map codified rules for an abstract map: building from an inflexible grid independent of geography, adjusting the map’s scale to account for discrepencies in station density, and aligning transit lines along regular horizontal, vertical, or 45-degree angles. This codification produced a highly-readable diagrammatic map whose influence is strongly felt to the present day.

London Underground Map by Fred Stingemore, 1928

Harry Beck's classic 1933 London Underground map

Altogether, we might create the following list of guidelines for generating a stylized, diagrammatic transit map:

• Angle/shape generalization – Line segments should be restricted to vertical, horizontal, and 45-degree angles, and shapes should be made regular where possible.
• Scale generalization – The scale of the map should be compressed in sparse areas and expanded in dense areas to maintain readability.
• Color-coded lines – Separate transit lines should be colored with separate, distinguishable colors.
• Intelligent labels – Sans-serif font, proper capitalization, and a predominately horizontal orientation.
• Topographic metadata – Large rivers, parks, or coastlines should appear as background elements to provide context for the map.
• Stations as symbols – Continuity of symbol should be used for individual stations. Dots, hashes, or circles are all suitable. Transfer points between lines should be clearly indicated, usually with a symbol that stretches to touch all the relevant lines.

Syott’s thesis is concerned with codifying these guidelines and writing software that will automatically generate transit maps given an arbitrary, geographic transit map.

Hill-climbing

A large portion of this thesis is dedicated to exploring and critiquing existing algorithms to automatically draw transit maps. Transit maps are but one example of a directed graph, that is, a set of nodes connected by a set of directed edges that each contain a weight (such as distance, or travel time). Since graphs are well-studied in the computer science literature, much of the research on visualizing graphs can also be used when visualizing transit maps.

The first step: Aligning nodes to the grid

Stott’s basic approach is to define a set of criteria for what might be considered a good transit map (as we have outlined above), and then use a hill-climbing algorithm to find an optimal visualization. He breaks the visualization strategy into multiple stages, starting with grid alignment and finishing with label placement.

At each phase, software “guesses” what a good map might be, and subsequently an evaluation function is run on the resulting map. If the current guess is better than the previous guess, then the software uses the current guess as the basis from which to generate its next guess. An optimal solution is reached when the algorithm has achieved a high score that other guesses are unable to best—that is to say, the algorithm will have reached the peak of the hill.

A full overview of this algorithm is beyond the scope of this review, but can be found in section 3 of the thesis.

Engaging tourists and travelers

Stott tests his computer-generated maps (a wide variety of city transit maps were used) by having individuals compare his maps with both their geographic and official counterparts. The results are mostly positive. Travelers find the diagrammatic maps on the whole to be better than their geographically-oriented counterparts. Computer generated maps tend to score against official maps, and many in fact preferred Stott’s maps to the official ones. The automatically-generated maps rate especially well when travelers were asked to estimate an optimal route from one place to another within a transit system.

Geographically accurate map of the DC Metro

Official DC Metro map

Stott's automatically-generated DC Metro map

Our evaluation: Stott’s DC Metro map is in many ways a better map than Metro’s official version. Stott’s map possesses greater resemblance to actual geography. The transfer stations and lines in central DC, especially around Metro Center and Federal Triangle are greatly distorted on the official map, whereas Stott’s version better captures the geographic relationships of these stations and their neighbors. Having lived in DC for some time, we are well acquainted with the scattering of downtown stations (many with multiple entrances), and Stott’s map neatly captures a lot of what we know from personal experience.

Stott’s maps are far from perfect, but are easily classified as good starting points that have massive head-starts on the traditional approach. In the case of the DC map, the adjustments might be simple: a green swath for Rock Creek Park, blue lines for the Potomac and Anacostia Rivers, adjustments to line weight, and perhaps label font and alignment.

Repurposing the transit map metaphor

As we briefly explored in our last post that described a stylized subway map of the web, a transit map metaphor is potentially useful in any number of network visualization or graph visualization tasks. Stott summarizes some examples of transit map visualizations.

Visualizing cancer pathways (Hahn and Weisberg, designed by Claudia Bentley)

In one example, a “trains of thought” metaphor demonstrates logical strands of argument woven through the author’s PhD thesis. Another example shows the route of a project plan from start to finish, highlighting intersections where key components need to be brought together. The most striking visualization is a map of cancer pathways (above).

Resources

• Download Jonathan Stott’s complete thesis (PDF, 366 pages. Oct 2008).
• Helpful distortion at NYC and London subway maps at 37Signals
• Edward Tufte on the London Underground map