A cartogram is a map where geographic areas are deliberately resized to reflect data rather than physical land area. Instead of showing countries or states at their true geographic scale, a cartogram stretches, shrinks, or replaces them with shapes whose size corresponds to a specific variable like population, GDP, or number of votes. The result looks like a funhouse mirror version of a familiar map, and that distortion is the whole point.
How Cartograms Differ From Standard Maps
On a traditional map, Russia dominates because it covers 17 million square kilometers. Canada looms large. India looks modest. But if you resize each country by population, India balloons to roughly four times the size of Russia, and Canada nearly vanishes. That shift in visual weight is what makes cartograms useful: they force the viewer to see data instead of geography.
The most common comparison is between a cartogram and a choropleth map, which is the standard colored-regions map you see in textbooks and news articles. A choropleth keeps geographic shapes accurate and uses color shading to represent data. The problem is that large, sparsely populated areas dominate the visual even when they represent a tiny fraction of the data. A cartogram solves this by making area itself carry the information, so a small but densely populated region gets the visual real estate it deserves.
Types of Cartograms
Contiguous Cartograms
These are the most recognizable type. Each region keeps its borders connected to neighboring regions, just as they are on a real map. The shapes stretch and warp to match the data, but the overall layout stays familiar enough that you can still identify most countries or states. The tradeoff is readability: heavily distorted regions can become unrecognizable, and labeling them is difficult. Algorithms that build contiguous cartograms try to preserve the original shapes as much as possible while hitting the target area for each region, but they can’t perfectly maintain every geographic relationship.
Non-Contiguous Cartograms
These take a different approach. Each region is resized independently and placed roughly where it belongs geographically, but gaps appear between them. You lose the shared borders, which makes the map feel less like a map, but individual shapes stay much closer to their original form. That makes them easier to identify at a glance.
Dorling Cartograms
Named after geographer Daniel Dorling, these replace each region entirely with a circle (or sometimes another simple shape) sized according to the data. The circles are arranged to approximate the original geographic layout, though their positions can drift significantly from the real map. What you gain is instant visual comparison: it’s easy to see which circles are bigger and to compare regions at a glance. What you lose is any resemblance to the actual shape of the territory.
Why Election Maps Are a Perfect Example
The most widely seen cartograms today are election maps. The familiar red-and-blue maps of U.S. presidential results are visually misleading because they show land area, not votes. A county in rural Montana and a county containing part of New York City get visual weight proportional to their acreage, not their population. The result is a sea of red with small blue dots, even in elections where the popular vote is nearly even or favoring the blue candidate.
Physicist Mark Newman at the University of Michigan created a well-known set of cartograms for the 2016 presidential election that rescaled states and counties by population. The difference is striking. Areas of red and blue become proportional to actual votes cast, giving a far more accurate picture of the political landscape. As researchers at the University of Connecticut’s Center for Land Use Education and Research put it, the standard method for displaying election results is “flawed” because it lets geography overpower the data. Cartograms correct that imbalance.
The Math Behind the Distortion
Building a contiguous cartogram is a surprisingly hard computational problem. The most influential method, published in the Proceedings of the National Academy of Sciences by Michael Gastner and Mark Newman, borrows from physics. It treats population density (or whatever variable you’re mapping) as if it were a substance that can diffuse, like heat spreading through metal. Regions with high density “push outward” while regions with low density “pull inward,” and the algorithm lets this process run until the density is perfectly even everywhere. The boundaries of each region ride along with this flow, stretching and compressing until every region’s area on the map is proportional to its data value.
Think of it this way: imagine each state is a balloon, and the air inside represents population. States with more people inflate, pushing against their neighbors. States with fewer people deflate. The algorithm figures out where every border point ends up once the pressure equalizes. The result is a map where visual size equals data value, with shapes that still loosely resemble the originals.
Strengths and Limitations
Cartograms are powerful because they make invisible patterns visible. They’re especially good at showing relationships between spatial units and making the magnitude of a variable immediately obvious. When you see a population cartogram where Bangladesh is larger than Australia, the data hits you in a way that a table of numbers never could.
But they come with real drawbacks. The most obvious is that distorted shapes are hard to recognize. If you’re not deeply familiar with the geography being shown, you may struggle to identify which blob is which, especially on contiguous cartograms without labels. Labeling itself is a challenge because warped polygons don’t always leave clean space for text. Cartograms also struggle with zero or negative values, since you can’t meaningfully shrink a region to nothing or less than nothing. And creating them requires more detailed boundary data than a simple colored map.
How to Create One
You don’t need to code a diffusion algorithm from scratch. Several tools handle cartogram creation for you. QGIS, a free and open-source geographic information system, has a plugin called cartogram3 that generates contiguous cartograms directly from polygon map layers. You load your map data, select the variable you want to visualize, and the plugin handles the distortion. ArcGIS, the commercial GIS standard, offers similar functionality. For simpler or web-based approaches, tools like the ScapeToad application and various JavaScript libraries (D3.js has cartogram extensions) let you build interactive cartograms without a full GIS setup.
The quality of the output depends heavily on the input data and the complexity of the geography. A cartogram of 50 U.S. states renders quickly and looks clean. A cartogram of 3,000 counties takes more processing power and produces a much harder-to-read result, which is why Dorling-style circle cartograms are often preferred for fine-grained data.