Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca - contact me Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca on Twitter Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca - Lumondo Photography Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca - Pi Art Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca - Hilbertonians - Creatures on the Hilbert CurveMartin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca - Pi Day 2020 - Piku
Lips that taste of tears, they say, are the best for kissing.Dorothy Parkerget crankymore quotes

3.14: beautiful


Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca
The Outbreak Poems — artistic emissions in a pandemic


visualization + design

“Transcendental Tree Map” from Yearning for the Infinite. This video premiered on 2020 Pi Day. Music by Max Cooper. Animation by Nick Cobby and myself.
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The 2020 Pi Day art celebrates digits of `\pi` with piku (パイク) —poetry inspired by haiku.
They serve as the form for The Outbreak Poems.
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A `\pi` day music video!: Transcendental Tree Map premieres on 2020 Pi Day from Max Cooper's Yearning for the Infinite. Animation by Nick Cobby and myself. Watch live from Barbican Centre.

`\pi` Day 2018 Art Posters - Stitched city road maps from around the world


Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2019 `\pi` has hundreds of digits, hundreds of languages and a special kids' edition.

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2018 `\pi` day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2017 `\pi` day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` approximation day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 `\pi` day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` approx day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 `\pi` day

Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Circular `\pi` art

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
All art posters are available for purchase.
I take custom requests.

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The roads in and around Copenhagen. (zoom)

In the zoom crop below, you can see the intersections (dots) and the individual polylines that connect the intersections.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Downtown Copenhagen. (zoom)

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).

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
In and around Christiansborg Slot (red dot) in downtown Copenhagen. (zoom)

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.


Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
On the road with 10 digits of `\pi`. City strips for Moscow, Mumbai, Nairobi, New Delhi, Nice, Prague, Rome, Stockholm, Vancouver and Warsaw. (BUY ARTWORK)

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Close-up of stitched streets in a city strip.

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.


Pi Day 2018 Art Posters  - Stitched city road maps from around the world
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
On the road with 36 digits of `\pi`. A world patch using Amsterdam, Doha, Marrakesh, Mumbai, Nairobi, Rome, San Francisco, Seoul, Shanghai and Vancouver (BUY ARTWORK)

Below I zoom in on patches in the center of the image and show the cities from which the patches were sampled.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Close-up of stitched streets in a world patch.

VIEW ALL

news + thoughts

Virus Mutations Reveal How COVID-19 Really Spread

Mon 04-05-2020

Genetic sequences of the coronavirus tell story of when the virus arrived in each country and where it came from.

Our graphic in Scientific American's Graphic Science section in the June 2020 issue shows a phylogenetic tree based on a snapshot of the data model from Nextstrain as of 31 March 2020.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Virus Mutations Reveal How COVID-19 Really Spread. Text by Mark Fischetti (Senior Editor), art direction by Jen Christiansen (Senior Graphics Editor), source: Nextstrain (enabled by data from GISAID).

Cover of Nature Cancer April 2020

Mon 27-04-2020

Our design on the cover of Nature Cancer's April 2020 issue shows mutation spectra of patients from the POG570 cohort of 570 individuals with advanced metastatic cancer.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Each ellipse system represents the mutation spectrum of an individual patient. Individual ellipses in the system correspond to the number of base changes in a given class and are layered by mutation count. Ellipse angle is controlled by the proportion of mutations in a class within the sample and its size is determined by a sigmoid mapping of mutation count scaled within the layer. The opacity of each system represents the duration since the diagnosis of advanced disease. (read more)

The cover design accompanies our report in the issue Pleasance, E., Titmuss, E., Williamson, L. et al. (2020) Pan-cancer analysis of advanced patient tumors reveals interactions between therapy and genomic landscapes. Nat Cancer 1:452–468.

Modeling infectious epidemics

Wed 06-05-2020

Every day sadder and sadder news of its increase. In the City died this week 7496; and of them, 6102 of the plague. But it is feared that the true number of the dead this week is near 10,000 ....
—Samuel Pepys, 1665

This month, we begin a series of columns on epidemiological models. We start with the basic SIR model, which models the spread of an infection between three groups in a population: susceptible, infected and recovered.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Modeling infectious epidemics. (read)

We discuss conditions under which an outbreak occurs, estimates of spread characteristics and the effects that mitigation can play on disease trajectories. We show the trends that arise when "flattenting the curve" by decreasing `R_0`.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Modeling infectious epidemics. (read)

This column has an interactive supplemental component that allows you to explore how the model curves change with parameters such as infectious period, basic reproduction number and vaccination level.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Modeling infectious epidemics. (Interactive supplemental materials)

Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: Modeling infectious epidemics. Nature Methods 17:455–456.

The Outbreak Poems

Sat 04-04-2020

I'm writing poetry daily to put my feelings into words more often during the COVID-19 outbreak.

That moment
when
you know a moment.
Branch to branch,
flit,
look everywhere,
chirp.
Memory,
scent
of thought fleeting.
Distant pasts
all
ways in plural
form.

Read the poems and learn what a piku is.

Deadly Genomes: Genome Structure and Size of Harmful Bacteria and Viruses

Tue 17-03-2020

A poster full of epidemiological worry and statistics. Now updated with the genome of SARS-CoV-2 and COVID-19 case statistics as of 3 March 2020.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Deadly Genomes: Genome Structure and Size of Harmful Bacteria and Viruses (zoom)

Bacterial and viral genomes of various diseases are drawn as paths with color encoding local GC content and curvature encoding local repeat content. Position of the genome encodes prevalence and mortality rate.

The deadly genomes collection has been updated with a posters of the genomes of SARS-CoV-2, the novel coronavirus that causes COVID-19.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Genomes of 56 SARS-CoV-2 coronaviruses that causes COVID-19.
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Ball of 56 SARS-CoV-2 coronaviruses that causes COVID-19.
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The first SARS-CoV-2 genome (MT019529) to be sequenced appears first on the poster.

Using Circos in Galaxy Australia Workshop

Wed 04-03-2020

A workshop in using the Circos Galaxy wrapper by Hiltemann and Rasche. Event organized by Australian Biocommons.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Using Circos in Galaxy Australia workshop. (zoom)

Download workshop slides.

Galaxy wrapper training materials, Saskia Hiltemann, Helena Rasche, 2020 Visualisation with Circos (Galaxy Training Materials).