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`\pi` Day 2018 Art Posters - Stitched city road maps from around the world
On March 14th celebrate `\pi` Day. Hug `\pi`—find a way to do it.
For those who favour `\tau=2\pi` will have to postpone celebrations until July 26th. That's what you get for thinking that `\pi` is wrong. I sympathize with this position and have `\tau` day art too!
If you're not into details, you may opt to party on July 22nd, which is `\pi` approximation day (`\pi` ≈ 22/7). It's 20% more accurate that the official `\pi` day!
Finally, if you believe that `\pi = 3`, you should read why `\pi` is not equal to 3.
And if you've got to sleep a moment on the road
I will steer for you
And if you want to work the street alone
I'll disappear for you
—Leonard Cohen (I'm Your Man)
This year's is the 30th anniversary of `\pi` day. The theme of the art is bridging the world and making friends. So myself I again team up with my long-time friend and collaborator Jake Lever. I worled with Jake on the snowflake catalogue, where we build a world of flakes.
And so, this year we also build a world. We start with all the roads in the world and stitch them together in brand new ways. And if you walk more than 1 km in this world, you'll likely to be transported somewhere completely different.
This year's `\pi` day song is Trance Groove: Paris. Why? Because it's worth to go to new places—real or imagined.
The input data set to the art are all the roads in the world, as obtained from Open Street Map.
Road segments between intersections are represented by polylines and ends at intersections are snapped together to coincide with a resolution of 5–10 meters.
There are 108,366,429 polylines and together they span about 39,930,000 km.
extracting cities
We took 44 cities and sampled a square patch of 0.6 × 0.6 degrees of roads from the data set centered on the longitude and latitude coordinates below. This roughly corresponds to a square of 65 km × 65 km.
These center coordinates might be slightly different from the canonical ones associated with a city—I used Google Maps to center the coordinates on what I felt was a useful center for sampling streets. Below are these coordinates along with the number of polylines extracted.
CITY LATITUDE LONGITUDE POLYLINES
--------------- ------------ ------------- ---------
amsterdam 52.38179720 4.90840330 98,965
bangkok 13.72635950 100.53609560 154,348
barcelona 41.38759720 2.17333560 86,575
beijing 39.90487690 116.39331750 49,867
berlin 52.51864170 13.40732310 64,336
buenos_aires -34.61566250 -58.50333750 267,432
cairo 30.05371250 31.23528970 108,524
copenhagen 55.67346250 12.58781160 45,025
doha 25.28233490 51.53479620 50,458
dublin 53.34316360 -6.24433520 44,109
edinburgh 55.94884870 -3.18828100 34,211
hong_kong 22.31338230 114.16994610 36,329
istanbul 41.03592820 28.98158110 190,938
jakarta -6.21858830 106.85252890 253,211
johannesburg -26.20653880 28.05113830 128,840
lisbon 38.73064000 -9.13667460 98,118
london 51.50838960 -0.08585320 169,164
los_angeles 34.04362360 -118.24505510 193,899
madrid 40.41671290 -3.70329570 112,495
marrakesh 31.63192610 -7.98895890 17,442
melbourne -37.88286720 145.11800540 140,817
mexico_city 19.39741470 -99.15827060 273,477
moscow 55.75202630 37.61531070 40,043
mumbai 19.18775070 72.97777590 65,316
nairobi -1.28718700 36.83157870 31,317
new_delhi 28.61245350 77.21369970 262,503
new_york 40.72187290 -73.92426750 199,652
nice 43.70006260 7.26974590 25,564
osaka 34.66944300 135.49965600 376,652
paris 48.85837360 2.29229260 175,028
prague 50.08022370 14.43002100 58,659
rome 41.89659480 12.49983650 81,370
san_francisco 37.77526950 -122.40966350 82,462
sao_paulo -23.57343700 -46.63341590 267,742
seoul 37.54869140 126.99479350 169,593
shanghai 31.22590500 121.47386710 50,036
st_petersburg 59.93029690 30.33955910 31,186
stockholm 59.32318770 18.07408060 48,321
sydney -33.86772020 151.20734660 76,820
tokyo 35.69220740 139.75613010 694,893
toronto 43.66328030 -79.38932030 73,173
vancouver 49.25782630 -123.19394300 34,081
vienna 48.20740250 16.37336040 53,669
warsaw 52.23101840 21.01639680 54,870
Each city's road coordinates were then transformed using the equirectangular projection to make the distance between longitude meridians constant with latitude. This was done by $$ \phi' \leftarrow \phi - \text{avg}(\phi) $$ $$ \lambda' \leftarrow (\lambda - avg(\lambda)) \text{cos} (avg(\phi)) $$
where `\phi` is the latitude and `\lambda` is the longitude. The average is taken over the patch of roads extracted for the city. For all steps below these transformed coordinates were used.
copenhagen
Let's look at one city—Copenhagen—to get a feel for the data set.
In the zoom crop below, you can see the intersections (dots) and the individual polylines that connect the intersections.
Zooming in even more you can see the Christiansborg Slot, one of the Danish Palaces and the seat of the Danish Parliament (corresponding Google Map view).
creating city strips
City strips were created by sampling patches of 0.015 × 0.015 degrees (after transformation). This corresponds roughly to 1.7 km.
For each position in the strip, patches were sampled in order of the digits of `\pi` only if the number of polylines in the was `40d \le N < 40(d+1)-1` where `d` is the digit of `\pi`. Patches for `d=9` only need to have `360 \le N` polylines.
For example, the first patch is assigned to `d=3` and it must have `120 \le N < 159` polylines. The second patch is sampled so that its density is `40 \le N < 79` because it is associated with the next digit, `d=1`.
Further selection on acceptable patches is performed so that the streets line up with the previous patch. Minor local adjustments and stitching are performed to make the join appear seamless.
Below is an example of a set of city strips for Amsterdam, Bangkok, Beijing, Berlin, Copenhagen, Edinburgh, Hong Kong, Johannesburg, Marrakesh and Melbourne.
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Below I zoom in on a portion of the city strips above to show the result of the stitching—individual street patches are outlined in blue squares.
It's interesting to see that some patches (e.g. 4th one on the bottom strip, which is Copenhagen) don't necessarily have roads that across the patch horizontally.
creating world patches
World patches are a two-dimension version of city strips but they use more than one city.
Patches are sampled from cities based on the order of the digits of `\pi`, as arranged on a 6 × 6 grid. For example, the first row of patches corresponds to 314159 and the second 265358. Each digit is assigned to a city from which the corresponding patch is sampled.
As for city strips, patches are selected only if they align with previous patches. This is now trickier to do in two-dimensions because we must match a selected patch with up to two other patches already placed.
Unlike for city strips, there is no selection made for street density.
Below is a world patch using the following digit-to-city assignment: 0:Amsterdam, 1:Doha, 2:Marrakesh, 3:Mumbai, 4:Nairobi, 5:Rome, 6:San Francisco, 7:Seoul, 8:Shanghai and 9:Vancouver.
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Below I zoom in on patches in the center of the image and show the cities from which the patches were sampled.
Beyond Belief Campaign BRCA Art
Fuelled by philanthropy, findings into the workings of BRCA1 and BRCA2 genes have led to groundbreaking research and lifesaving innovations to care for families facing cancer.
This set of 100 one-of-a-kind prints explore the structure of these genes. Each artwork is unique — if you put them all together, you get the full sequence of the BRCA1 and BRCA2 proteins.
Propensity score weighting
The needs of the many outweigh the needs of the few. —Mr. Spock (Star Trek II)
This month, we explore a related and powerful technique to address bias: propensity score weighting (PSW), which applies weights to each subject instead of matching (or discarding) them.
Kurz, C.F., Krzywinski, M. & Altman, N. (2025) Points of significance: Propensity score weighting. Nat. Methods 22:1–3.
Happy 2025 π Day—
TTCAGT: a sequence of digits
Celebrate π Day (March 14th) and sequence digits like its 1999. Let's call some peaks.
Crafting 10 Years of Statistics Explanations: Points of Significance
I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player
Points of Significance is an ongoing series of short articles about statistics in Nature Methods that started in 2013. Its aim is to provide clear explanations of essential concepts in statistics for a nonspecialist audience. The articles favor heuristic explanations and make extensive use of simulated examples and graphical explanations, while maintaining mathematical rigor.
Topics range from basic, but often misunderstood, such as uncertainty and P-values, to relatively advanced, but often neglected, such as the error-in-variables problem and the curse of dimensionality. More recent articles have focused on timely topics such as modeling of epidemics, machine learning, and neural networks.
In this article, we discuss the evolution of topics and details behind some of the story arcs, our approach to crafting statistical explanations and narratives, and our use of figures and numerical simulations as props for building understanding.
Altman, N. & Krzywinski, M. (2025) Crafting 10 Years of Statistics Explanations: Points of Significance. Annual Review of Statistics and Its Application 12:69–87.
Propensity score matching
I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player
In many experimental designs, we need to keep in mind the possibility of confounding variables, which may give rise to bias in the estimate of the treatment effect.
If the control and experimental groups aren't matched (or, roughly, similar enough), this bias can arise.
Sometimes this can be dealt with by randomizing, which on average can balance this effect out. When randomization is not possible, propensity score matching is an excellent strategy to match control and experimental groups.
Kurz, C.F., Krzywinski, M. & Altman, N. (2024) Points of significance: Propensity score matching. Nat. Methods 21:1770–1772.
Understanding p-values and significance
P-values combined with estimates of effect size are used to assess the importance of experimental results. However, their interpretation can be invalidated by selection bias when testing multiple hypotheses, fitting multiple models or even informally selecting results that seem interesting after observing the data.
We offer an introduction to principled uses of p-values (targeted at the non-specialist) and identify questionable practices to be avoided.
Altman, N. & Krzywinski, M. (2024) Understanding p-values and significance. Laboratory Animals 58:443–446.