4 ms·

A hexagonal-tiled cartogram for U.S. counties

63 points by jordanhroga 2y ago

A direct link to the data used: https://github.com/jordanroga/hex-cartogram/blob/main/County%20Hex%20Cartogram.csv https://github.com/jordanroga/hex-cartogram/blob/main/County....

deleted 2y ago
[deleted]
jasongill 2y ago
I am not a cartographer or any type of a data visualization expert, but isn't the advantage of the hexagon map - the fact that it "highlights trends that are often masked by the geographical quirks of actual state boundaries" per the article - negated by hexagon county maps? For example, California has 58 counties, but Kentucky has 120. That means that the "resolution" of the data in California is half as accurate as the data in Kentucky despite having ten times as many inhabitants and 4 times the land area. Basically, by switching to hexagon county maps, aren't we actually amplifying the problem that hexagon state maps try to solve and making it worse, not better? (A good article and good examples OP but I just don't personally see how the hexagon county map is an improvement, but again I am not an expert in this field)
- secabeen 2y ago
  > For example, California has 58 counties, but Kentucky has 120. That means that the "resolution" of the data in California is half as accurate as the data in Kentucky despite having ten times as many inhabitants and 4 times the land area. Kentucky also simply looks larger, which over-indexes its importance. I can't really think of any data that I would want visualized by county directly, especially data about people. In California alone, there is a 9000:1 population variance between the largest and smallest county.
- standardUser 2y ago
  It helps if you have a dataset that goes by county, and a lot of data in the US has it's highest resolution at the county level.
- jordanhroga 2y ago
  You're correct that increasing resolution to the county level can inflate the size of states with more counties. This kind of map wouldn't be appropriate for a state by state comparison at all; instead, it's more useful for a county by county comparison. It's just a different resolution of administrative boundary and there are limits to that. A lot of U.S. data is reported at the county level and comparing across regions within or across states without worrying about the geography or shapes of different counties can sometimes be helpful. Adding population as a size dimension and filtering to a single state can also help mitigate the distortions.
- cyberax 2y ago
  ZIP codes or Census blocks would be better, but very few datasets go into that level of detail.
  - mistrial9 2y ago
    ZIP codes (ZCTA) are uniquely awful for many reasons.. It would be better to avoid them when possible IMHO
    - wolfgang42 2y ago
      Yeah, an important but little-understood fact about ZIP codes is that they are not an area, but a collection of points (≈mailboxes) and polylines (delivery routes); this is because they were created by the post office, who care about logistics, not land. You can try to impute geographical location from them and this mostly works, but there are fun edge cases such as an area where the streets going in one direction are in one ZIP code and all of the cross streets in a different one. The code for an address can also be changed at USPS’s convenience (making comparisons over time difficult); in extremely rural areas “your ZIP code” may be whichever town you prefer to pick your mail up from. (My favorite fun fact about ZIP codes: 12345 is the General Electric headquarters and factory in Schenectady, New York. They get a lot of mail addressed to Santa Claus.)
ge96 2y ago
side note Uber wrote about hexagons https://www.uber.com/blog/h3/ https://www.uber.com/blog/h3/ I also remember a star link map with hexagons
- ZeWaka 2y ago
  Starlink's availability map uses hexagons, but you likely mean https://satellitemap.space/ https://satellitemap.space/
  - ajfriend 2y ago
    That map does seem to be using H3 hexagons: https://h3geo.org/ https://h3geo.org/
  - ge96 2y ago
    Yeah that's a cool site too but actually I was thinking of this super detailed post https://mikepuchol.com/modeling-starlink-capacity-843b2387f501 https://mikepuchol.com/modeling-starlink-capacity-843b2387f5...
Onavo 2y ago
How are you generating it? A modified voronoid?
- jordanhroga 2y ago
  I just went in and manually played around with what I thought made sense. The primary consideration was what counties were nearest each other county and secondarily what the shape of the state was. I also factored in to some degree what counties were near others across state lines, but the number of counties not reflecting geographical sizes meant this was a bit challenging to keep consistent. I did my best though.
dragonwriter 2y ago
> Hexagons have a unique property: they tile a plane without gaps, and each cell maintains a consistent shape and size. This is not a unique feature of hexagons; squares do this (and square-tiled cartograms are common, and to the extent any thing in this article is a real trait of hex-tiled cartograms it also is of square-tiled ones) as do triangles (though you need two different orientations with triangles.) > Compared to square grids, hexagonal tiling reduces the “edge effect” where corners in squares can mislead the interpretation of adjacency. This is true if you are drawing a grid over a true map, but when you make a cartogram that reduces irregularly sized and shaped geographic units (counties) to each be represented by any regular polygon, you are going to "mislead the interpretation of adjacency" pretty significantly in any case, so this seems largely irrelevant to the presented use case.
dmurray 2y ago
> A county like San Francisco or New York, which packs thousands of residents into a small area, now stands out with an intense color saturation, drawing the eye immediately to where the people actually are. Conversely, a vast county with a sparse population adopts a lighter tone, accurately reflecting its lower density without the distraction of an oversized area. That sounds great, but this colour scheme doesn't seem to be what was actually used on the map. If I know anything about the US population density, the gradient used is dark blue -> light blue -> light pink -> red, so the "vast counties with sparse population" actually show up as saturated as the dense urban ones. The most visually attractive areas on that map are the large dark blue areas of West Texas and the Rockies, the opposite of the intention described in the text. I would recommend using a single colour gradient instead.
- jordanhroga 2y ago
  Initially I had put a single color gradient, but I updated the graph because high density areas weren't standing out enough relatively. Updated the text to reflect the updated graph.
philsnow 2y ago
The first image jumped out at me because the author chose to use blue and red which, when used on a map of the United States always indicates political affiliation, but the areas that were marked "red" and "blue" were reversed from what my expectation was (coasts and cities red, midwest + great plains blue). > A county like San Francisco or New York, which packs thousands of residents into a small area, now stands out with an intense color saturation, drawing the eye immediately to where the people actually are. Conversely, a vast county with a sparse population adopts a lighter tone, accurately reflecting its lower density without the distraction of an oversized area. (Emphasis on "saturation" added.) This isn't quite right, the most-densely populated hexes (large cities) are a pretty saturated red color yes, but the least-densely populated hexes (west Texas) are a pretty saturated blue color. In fact, this color palette makes it really difficult to see what the author intends. > Using the size of counties as a dimension to represent population can also showcase population centers and free up the color dimension to show another dimension like population density. Ok yeah that's a cartogram, I know how to expect that to look... wait, no, the image has the same center points for every county, a hexagon outline drawn around that, and then a confusingly-colored solid circle painted over each. The colors are confusing because the overwhelming effect is that the hex outlines dominate the perception of the dark blue nearly-point-sized "circles" in the majority of the map. Look at Nevada. On the first map Clark County (where Las Vegas is) is a light blue colored hex in a state of mostly dark blue hexes and Washoe County (where Reno is) is light red. On the second map Clark is the largest light blue circle in the state and Washoe is a smaller light blue circle, which seems to be the reverse of what the first map says. ...Also, Washoe appears to be in a different place maybe? It seems to have moved north a hex. I'm not just picking nits, this is difficult stuff, but an extremely powerful way to convey a ton of densely-packed (no pun intended) information, when done right. See, for instance [0][1][2][3] all by Edward Tufte. [0] "The Visual Display of Quantitative Information" https://www.amazon.com/Visual-Display-Quantitative-Information/dp/0961392142 https://www.amazon.com/Visual-Display-Quantitative-Informati... [1] "Visual Explanations: Images and Quantities, Evidence and Narrative" https://www.amazon.com/dp/0961392126 https://www.amazon.com/dp/0961392126 [2] "Beautiful Evidence" https://www.amazon.com/dp/0961392177 https://www.amazon.com/dp/0961392177 [3] "Envisioning Information" https://www.amazon.com/Envisioning-Information-Edward-R-Tufte/dp/0961392118 https://www.amazon.com/Envisioning-Information-Edward-R-Tuft...
crazygringo 2y ago
I'm struggling to think of a use case for this. Hexagonal maps make sense for values where geographical size is irrelevant and you're not controlling for population size. So state-level hexagonal maps make sense for showing the red/blue color of US senators, for example. (Technically each hexagon gets split in half, since there are 2 senators.) And you could do a hexagonal map for Congressional districts as well. Or state-level legislative districts within states. Because each area has equal political power, and so it makes sense they have the same area. But I'm struggling to think of a situation where you'd ever want to do this at a county level. If you want to draw things like population density, then you can shade by people per square mile or similar, within normal geographic boundaries, and there's no distortion. Or any kind of rate per capita, then you just shade the normal geographic boundaries at a per-capita rate. And if you want it to also be population map, you need to resize areas proportionally to population, like this: https://www.vox.com/2015/8/19/9178979/united-states-population https://www.vox.com/2015/8/19/9178979/united-states-populati... But that's the opposite of making things the same size. But I can't think of a single county-level statistic where there's a good reason to make counties all the same size. Can anyone else?
dmwood 2y ago
As noted, ordinary maps may suffer (for example, in epidemiology)from the impact of a very non-uniform population density. A disease cluster then MAY be a cluster, or it may be ordinary disease rates in a highly populated area. In my limited experience a cartogram is a deliberate distortion of the SHAPE of a map region in order to make some property (say, population DENSITY) constant everywhere in the new region. Then anomalies jump out. Done with care, one can do careful statistics within the cartogram and then back-transform to get statistics for the original map area.
wosk 2y ago
Very cool, that's an interesting and useful visualization. I work in infectious disease forecasting, and I wanted to give it a try already. However, the csv columns are `State,County Name,x,y,Color,...,Largest City,County Full,State Full` whereas our US model outputs are expressed using census geoids[1] (5-digits for county), and I believe that would also be the case for other potential users. In that case one would need to merge with the county dataframe[2] [1] https://www.census.gov/programs-surveys/geography/guidance/geo-identifiers.html https://www.census.gov/programs-surveys/geography/guidance/g... [2] https://www2.census.gov/geo/docs/reference/codes/files/national_county.txt https://www2.census.gov/geo/docs/reference/codes/files/natio...

63 points by jordanhroga 2y ago

A direct link to the data used: https://github.com/jordanroga/hex-cartogram/blob/main/County%20Hex%20Cartogram.csv https://github.com/jordanroga/hex-cartogram/blob/main/County....

deleted 2y ago

[deleted]

jasongill 2y ago

I am not a cartographer or any type of a data visualization expert, but isn't the advantage of the hexagon map - the fact that it "highlights trends that are often masked by the geographical quirks of actual state boundaries" per the article - negated by hexagon county maps? For example, California has 58 counties, but Kentucky has 120. That means that the "resolution" of the data in California is half as accurate as the data in Kentucky despite having ten times as many inhabitants and 4 times the land area. Basically, by switching to hexagon county maps, aren't we actually amplifying the problem that hexagon state maps try to solve and making it worse, not better? (A good article and good examples OP but I just don't personally see how the hexagon county map is an improvement, but again I am not an expert in this field)

secabeen 2y ago
> For example, California has 58 counties, but Kentucky has 120. That means that the "resolution" of the data in California is half as accurate as the data in Kentucky despite having ten times as many inhabitants and 4 times the land area. Kentucky also simply looks larger, which over-indexes its importance. I can't really think of any data that I would want visualized by county directly, especially data about people. In California alone, there is a 9000:1 population variance between the largest and smallest county.
standardUser 2y ago
It helps if you have a dataset that goes by county, and a lot of data in the US has it's highest resolution at the county level.
jordanhroga 2y ago
You're correct that increasing resolution to the county level can inflate the size of states with more counties. This kind of map wouldn't be appropriate for a state by state comparison at all; instead, it's more useful for a county by county comparison. It's just a different resolution of administrative boundary and there are limits to that. A lot of U.S. data is reported at the county level and comparing across regions within or across states without worrying about the geography or shapes of different counties can sometimes be helpful. Adding population as a size dimension and filtering to a single state can also help mitigate the distortions.
cyberax 2y ago
ZIP codes or Census blocks would be better, but very few datasets go into that level of detail.
- mistrial9 2y ago
  ZIP codes (ZCTA) are uniquely awful for many reasons.. It would be better to avoid them when possible IMHO
  - wolfgang42 2y ago
    Yeah, an important but little-understood fact about ZIP codes is that they are not an area, but a collection of points (≈mailboxes) and polylines (delivery routes); this is because they were created by the post office, who care about logistics, not land. You can try to impute geographical location from them and this mostly works, but there are fun edge cases such as an area where the streets going in one direction are in one ZIP code and all of the cross streets in a different one. The code for an address can also be changed at USPS’s convenience (making comparisons over time difficult); in extremely rural areas “your ZIP code” may be whichever town you prefer to pick your mail up from. (My favorite fun fact about ZIP codes: 12345 is the General Electric headquarters and factory in Schenectady, New York. They get a lot of mail addressed to Santa Claus.)

ge96 2y ago

side note Uber wrote about hexagons https://www.uber.com/blog/h3/ https://www.uber.com/blog/h3/ I also remember a star link map with hexagons

ZeWaka 2y ago
Starlink's availability map uses hexagons, but you likely mean https://satellitemap.space/ https://satellitemap.space/
- ajfriend 2y ago
  That map does seem to be using H3 hexagons: https://h3geo.org/ https://h3geo.org/
- ge96 2y ago
  Yeah that's a cool site too but actually I was thinking of this super detailed post https://mikepuchol.com/modeling-starlink-capacity-843b2387f501 https://mikepuchol.com/modeling-starlink-capacity-843b2387f5...

Onavo 2y ago

How are you generating it? A modified voronoid?

jordanhroga 2y ago
I just went in and manually played around with what I thought made sense. The primary consideration was what counties were nearest each other county and secondarily what the shape of the state was. I also factored in to some degree what counties were near others across state lines, but the number of counties not reflecting geographical sizes meant this was a bit challenging to keep consistent. I did my best though.

dragonwriter 2y ago

> Hexagons have a unique property: they tile a plane without gaps, and each cell maintains a consistent shape and size. This is not a unique feature of hexagons; squares do this (and square-tiled cartograms are common, and to the extent any thing in this article is a real trait of hex-tiled cartograms it also is of square-tiled ones) as do triangles (though you need two different orientations with triangles.) > Compared to square grids, hexagonal tiling reduces the “edge effect” where corners in squares can mislead the interpretation of adjacency. This is true if you are drawing a grid over a true map, but when you make a cartogram that reduces irregularly sized and shaped geographic units (counties) to each be represented by any regular polygon, you are going to "mislead the interpretation of adjacency" pretty significantly in any case, so this seems largely irrelevant to the presented use case.

dmurray 2y ago

> A county like San Francisco or New York, which packs thousands of residents into a small area, now stands out with an intense color saturation, drawing the eye immediately to where the people actually are. Conversely, a vast county with a sparse population adopts a lighter tone, accurately reflecting its lower density without the distraction of an oversized area. That sounds great, but this colour scheme doesn't seem to be what was actually used on the map. If I know anything about the US population density, the gradient used is dark blue -> light blue -> light pink -> red, so the "vast counties with sparse population" actually show up as saturated as the dense urban ones. The most visually attractive areas on that map are the large dark blue areas of West Texas and the Rockies, the opposite of the intention described in the text. I would recommend using a single colour gradient instead.

jordanhroga 2y ago
Initially I had put a single color gradient, but I updated the graph because high density areas weren't standing out enough relatively. Updated the text to reflect the updated graph.

philsnow 2y ago

The first image jumped out at me because the author chose to use blue and red which, when used on a map of the United States always indicates political affiliation, but the areas that were marked "red" and "blue" were reversed from what my expectation was (coasts and cities red, midwest + great plains blue). > A county like San Francisco or New York, which packs thousands of residents into a small area, now stands out with an intense color saturation, drawing the eye immediately to where the people actually are. Conversely, a vast county with a sparse population adopts a lighter tone, accurately reflecting its lower density without the distraction of an oversized area. (Emphasis on "saturation" added.) This isn't quite right, the most-densely populated hexes (large cities) are a pretty saturated red color yes, but the least-densely populated hexes (west Texas) are a pretty saturated blue color. In fact, this color palette makes it really difficult to see what the author intends. > Using the size of counties as a dimension to represent population can also showcase population centers and free up the color dimension to show another dimension like population density. Ok yeah that's a cartogram, I know how to expect that to look... wait, no, the image has the same center points for every county, a hexagon outline drawn around that, and then a confusingly-colored solid circle painted over each. The colors are confusing because the overwhelming effect is that the hex outlines dominate the perception of the dark blue nearly-point-sized "circles" in the majority of the map. Look at Nevada. On the first map Clark County (where Las Vegas is) is a light blue colored hex in a state of mostly dark blue hexes and Washoe County (where Reno is) is light red. On the second map Clark is the largest light blue circle in the state and Washoe is a smaller light blue circle, which seems to be the reverse of what the first map says. ...Also, Washoe appears to be in a different place maybe? It seems to have moved north a hex. I'm not just picking nits, this is difficult stuff, but an extremely powerful way to convey a ton of densely-packed (no pun intended) information, when done right. See, for instance [0][1][2][3] all by Edward Tufte. [0] "The Visual Display of Quantitative Information" https://www.amazon.com/Visual-Display-Quantitative-Information/dp/0961392142 https://www.amazon.com/Visual-Display-Quantitative-Informati... [1] "Visual Explanations: Images and Quantities, Evidence and Narrative" https://www.amazon.com/dp/0961392126 https://www.amazon.com/dp/0961392126 [2] "Beautiful Evidence" https://www.amazon.com/dp/0961392177 https://www.amazon.com/dp/0961392177 [3] "Envisioning Information" https://www.amazon.com/Envisioning-Information-Edward-R-Tufte/dp/0961392118 https://www.amazon.com/Envisioning-Information-Edward-R-Tuft...

crazygringo 2y ago

I'm struggling to think of a use case for this. Hexagonal maps make sense for values where geographical size is irrelevant and you're not controlling for population size. So state-level hexagonal maps make sense for showing the red/blue color of US senators, for example. (Technically each hexagon gets split in half, since there are 2 senators.) And you could do a hexagonal map for Congressional districts as well. Or state-level legislative districts within states. Because each area has equal political power, and so it makes sense they have the same area. But I'm struggling to think of a situation where you'd ever want to do this at a county level. If you want to draw things like population density, then you can shade by people per square mile or similar, within normal geographic boundaries, and there's no distortion. Or any kind of rate per capita, then you just shade the normal geographic boundaries at a per-capita rate. And if you want it to also be population map, you need to resize areas proportionally to population, like this: https://www.vox.com/2015/8/19/9178979/united-states-population https://www.vox.com/2015/8/19/9178979/united-states-populati... But that's the opposite of making things the same size. But I can't think of a single county-level statistic where there's a good reason to make counties all the same size. Can anyone else?

dmwood 2y ago

As noted, ordinary maps may suffer (for example, in epidemiology)from the impact of a very non-uniform population density. A disease cluster then MAY be a cluster, or it may be ordinary disease rates in a highly populated area. In my limited experience a cartogram is a deliberate distortion of the SHAPE of a map region in order to make some property (say, population DENSITY) constant everywhere in the new region. Then anomalies jump out. Done with care, one can do careful statistics within the cartogram and then back-transform to get statistics for the original map area.

wosk 2y ago

Very cool, that's an interesting and useful visualization. I work in infectious disease forecasting, and I wanted to give it a try already. However, the csv columns are `State,County Name,x,y,Color,...,Largest City,County Full,State Full` whereas our US model outputs are expressed using census geoids[1] (5-digits for county), and I believe that would also be the case for other potential users. In that case one would need to merge with the county dataframe[2] [1] https://www.census.gov/programs-surveys/geography/guidance/geo-identifiers.html https://www.census.gov/programs-surveys/geography/guidance/g... [2] https://www2.census.gov/geo/docs/reference/codes/files/national_county.txt https://www2.census.gov/geo/docs/reference/codes/files/natio...