Warning: sensitive souls who care about geodetic accuracy should probably stop reading now. Liberal use of affine transformation of geometries throughout. You have been warned.
Before I get going, huge appreciation to Randall Munroe for the generous terms of use for the XKCD comics.
For a long time I thought about teaching a geography / GIS class using XKCD comics as the primary source material, or at the very least as a jumping off point for every lecture. Recently I actually went through every XKCD from the very beginning to the present to assemble a list of comics that would actually be usable in some semi-serious2 way for this purpose. Among the things I learned is that Randall Munroe has become a lot less fixated on sex than he was when he started, and also somewhat less worried about velociraptors.
Also, his interest in map projections only seems to have kicked in about halfway through the XKCD time series. Possibly this is related to an ongoing interest in GPS, which will likely be a topic for a future post. #977 Map projections posted in late 2011, is the first sign of an enduring interest in projections, but things don’t really take off until #1500 almost 4 years later, which is the first of several ‘bad map projections’, although not actually called out as such in its title.
Herewith, my ranking from worst bad projection to best bad projection of the nine examples I found,3 accompanied in a few cases by attempts at recreating them in R (click on the code-fold links to see how). Eventually, perhaps, ongoing work on arbitrary map projections might enable me to automate reverse-engineering any XKCD projection. For now, a combination of perseverance, guess-work, and sheer bloody mindedness will have to suffice.
library(sf)
library(tmap)
library(usmap)
library(dplyr)
library(ggplot2)
library(stringr)
library(smoothr)
library(xkcd)World dataset.
usmap::us_map().
densify some shapes.
For what it’s worth, by worst bad projection I mean something like ‘least interesting’ and by best, I mean something like ‘most thought-provoking’.4
I don’t use Adobe Photoshop so XKCD 1784 is just a bit too inside baseball for me. It feels like there might be a missed opportunity here to have said something about continental drift and Pangaea and supercontinents, which is a topic that has come up in other XKCDs (see # 1449 Red Rover). Something about how Africa and South America fitting together so well is evidence for plate tectonics liquid resize.
XKCD 2999 just doesn’t work for me.5 I appreciate the attempt at many to one projection, that is to say more than one place on Earth mapping onto a single location in the map. And it’s certainly a relief to know that Melbourne is preserved.6
I didn’t even try to replicate this one as it seems self-evidently something you’d have to do in a drawing package. Overall, I think the idea of two places into one is much better realised elsewhere in this list.
The whole Greenland thing in map projections is a bit played out. I realise it continues to blow minds how exaggerated its size is in the Mercator projection.7 Anyway, it’s not too hard to remake XKCD 2489 using R, provided you aren’t too respectful of, you know, actual projections. Apparently Mercator Greenland is too big even for this comedy projection, as I had to downscale it to 85% of its ‘raw’ Mercator size to get a good match to the published map.
greenland <- World |>
filter(name == "Greenland") |>
st_transform("+proj=merc") |>
mutate(geometry =
(geometry + c(2e6, -3.1e6)) * diag(1, 2, 2) * 0.85) |>
st_set_crs("+proj=merc")
greenland_buffer <- greenland |>
st_buffer(1e5)
w <- World |>
st_transform("+proj=moll") |>
st_make_valid() |>
st_set_crs("+proj=merc") |>
st_difference(greenland_buffer) |>
bind_rows(greenland)
ggplot(w) +
geom_sf() +
coord_sf(xlim = c(-1.2e7, 1.7e7), expand = FALSE) +
theme_void()
XKCD 2613 went up in my estimation after I figured out how to make it… the alt-text provides enough information to find the central coordinates, which are in La Gogue Lake on Mahé in the Seychelles.
Armed with the ludicrously precise lat-lon coordinates8 Google provided me for this spot, I figured out how to approximate this map.
ll <- c(-4.595750619515433, 55.43837198904654)
madagascator <- World |>
st_transform(str_glue("+proj=laea +lon_0={ll[2]} +lat_0={ll[1]}")) |>
st_set_crs("+proj=laea +lon_0=150 +lat_0=90") |>
st_transform("+proj=merc")
ggplot(madagascator) +
geom_sf(fill = "lightgrey",
color = "darkgrey") +
geom_sf_text(aes(label = name),
check_overlap = TRUE,
size = 3) +
theme_void()sf that the data are centred on somewhere different than they really are! Some experimentation was required here to find a central ‘meridian’ that didn’t cut Antarctica in half.
+proj=omerc) that can do this sequence of transforms in one go, but since what I have works, I am leaving well alone.
XKCD 2256 is just delightfully dumb really. Truly a bad map projection. It’s also hard (for me) not to love a map projection that will throw everyone doing Worldle off their game.
The ‘comical’ claim about topologists in the alt-text for XKCD 2951 is actually… well… true on a spherical surface.
I figured out a way to approximate this projection. First, we project the contiguous 48 states centred on the geographic center and enlarge them so they ostensibly cover a greater part of Earth’s surface. Any projection should work here; I’ve used an azimuthal equidistant one.
ctr <- c(-98.583333, 39.833333)
anti <- c(ctr[1] + 180, -ctr[2])
proj1 <- str_glue("+proj=aeqd +lon_0={ctr[1]} +lat_0={ctr[2]}")
proj2 <- str_glue("+proj=aeqd +lon_0={anti[1]} +lat_0={anti[2]}")
states_big <- usmap::us_map() |>
rename(geometry = geom) |>
smoothr::densify(20) |>
filter(!(abbr %in% c("AK", "HI"))) |>
st_transform(proj1) |>
mutate(geometry = geometry * matrix(c(5, 0, 0, 5), 2, 2)) |>
st_set_crs(proj1)
ggplot(states_big) + geom_sf() + theme_minimal()
Next we apply an azimuthal equidistant projection centred on the antipode of the geographical centre. At this point we have to ‘turn Kansas inside out’, then remove and add it back into the inverted states.
states_inv <- states_big |>
st_transform(proj2)
kansas <- states_inv |>
st_bbox() |>
st_as_sfc() |>
as.data.frame() |>
st_as_sf() |>
st_difference(states_inv |>
filter(abbr == "KS")) |>
st_as_sf()
states_inv <- states_inv |>
filter(abbr != "KS") |>
bind_rows(kansas)And now we can make the final map. Note that it seems like an adjustment to the aspect ratio has been applied in the comic. I’ve not bothered with that step here. I assume that at some point Randall Munroe exports map data to a drawing package and does final tweaks there.
ggplot(states_inv) +
geom_sf(fill = "white") +
geom_sf_text(
data = states_inv |> st_point_on_surface(),
aes(label = full), check_overlap = TRUE, size = 3) +
coord_sf(expand = FALSE) +
theme_void() +
theme(panel.background = element_rect(fill = "grey"),
panel.border = element_rect(fill = NA, colour = "black",
linewidth = 1))
Personally, living in Aotearoa New Zealand I enjoy the genre of ‘upside down’ maps, but have always felt that the notion they change your whole perspective on the world is overstated, so XKCD 1500 is a nice gentle undermining of that, which I appreciate.9
I briefly contemplated an attempt at making this one, but thought better of it. Turning a whole map through 180° is not difficult:
w180 <- World |>
mutate(geometry = geometry * diag(-1, 2, 2)) |>
st_set_crs(4326) |>
st_transform("+proj=eqearth")
ggplot(w180) +
geom_sf() +
coord_sf(expand = FALSE) +
theme_minimal()
Likely the easiest way to make this into a map like the one in the comic is to export to a drawing format and move things around by hand.
If only rendering XKCD 2807 was as easy as doing longitude = abs(longitude).10 In R things get a bit more involved. This would really be very straightforward in a drawing package.
get_hemisphere <- function(central_meridian = 0,
density = 1) {
lons <- c( 1, 1, -1, -1, 1) * 90 + central_meridian
lats <- c(-1, 1, 1, -1, -1) * 90
st_polygon(list(matrix(c(lons, lats), ncol = 2))) |>
st_sfc() |>
as.data.frame() |>
st_as_sf(crs = 4326) |>
smoothr::densify(density)
}
proj = "+proj=eqearth"
hemi_w <- get_hemisphere(-90)
hemi_e <- get_hemisphere(90)
world_w <- World |>
st_intersection(hemi_w) |>
mutate(geometry = geometry * matrix(c(-1, 0, 0, 1), 2, 2)) |>
st_set_crs(4326)
world_e <- World |>
st_intersection(hemi_e)
world_abs <- world_w |>
bind_rows(world_e) |>
mutate(id = 1) |>
group_by(id) |>
summarise() |>
mutate(geometry = geometry - c(90, 0)) |>
st_set_crs(4326) |>
st_transform(proj)
half_globe <- get_hemisphere(density = 50) |>
st_transform(proj)
ggplot() +
geom_sf(data = half_globe, lwd = 0) +
geom_sf(data = world_abs, fill = "white") +
geom_sf(data = half_globe, fill = NA, lwd = 1) +
coord_sf(expand = FALSE) +
theme_void()density parameter gives us hemispheres that still look right after transformation to a non-rectangular projection.
I’m really not convinced XKCD 1799 is a bad map projection. It looks wonky as hell, but it’s certainly useful, which is all we can ask of any projection.11 I’m fairly confident Waldo Tobler would have approved, although I never had an opportunity to ask.
It’s interesting to contemplate what kind of automated process might be used to produce this map, but… I’m not even going to try. Happy to hear from anyone who gives it a go!
Close analysis of the data confirms no clear long term trend in the badness of XKCD’s bad map projections, although more recent examples may be getting worse.12
And that’s a wrap (or fold, or cut, or… some transformation anyway).
Insert ‘You won’t believe how bad they are’ or similar clickbait headline here.↩︎
We’re working with a loose definition of the word ‘serious’ here.↩︎
Along with #1500 which was not called out as such↩︎
YMMV. Don’t @ me.↩︎
I’d obviously rank it higher if it was called United Straya.↩︎
I have relatives there.↩︎
Maybe someone should have a word with a recently elected president on this matter.↩︎
I’m not sure how I feel about ‘The United Kingdom of Great Britain and Southern Ireland’, but that’s a whole other question…↩︎
Or for that matter, model…↩︎
The same analysis suggests that while negative ranks are a possibility they remain unlikely.↩︎