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
Drive, driven. Gave, given.YelloGive me a number of games.more quotes

pi: 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` Approximation Day Art Posters


Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2019 `\pi` has hundreds of digits, hundreds of languages and a special kids' edition.

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2018 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2017 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` approximation day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` approx day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Circular `\pi` art

The never-repeating digits of `\pi` can be approximated by 22/7 = 3.142857 to within 0.04%. These pages artistically and mathematically explore rational approximations to `\pi`. This 22/7 ratio is celebrated each year on July 22nd. If you like hand waving or back-of-envelope mathematics, this day is for you: `\pi` approximation day!

Want more math + art? Discover the Accidental Similarity Number. Find humor in my poster of the first 2,000 4s of `\pi`.

There are two kinds of `\pi` Approximation Day posters.

The first uses the Archimedean spiral for its design, which I've used before for other numerical art. The second packs warped circles, whose ratio of circumference to average diameter is `22/7` into what I call `\pi`-approximate circular packing.

As you probably know, the ratio of the circumference of a circle to its diameter is `\pi`. $$ C / d = \pi $$

For `\pi` approximation day, let's ask what would happen if $$ C / d = 22/7 $$

where now `C` is the circumference of some shape other than a circle. What could this shape be?

A good place to start is to think about an ellipse. I've done this before in the 22/7 Universe article, in which I considered an ellipse with a major axis of `r+\delta` and a minor axis of `r` and solved for `\delta` such that the circumference of the ellipse divided by `2 r` would be `22/7`. Doing so means numerically solving the equation $$ \frac{C(r,r+\delta)}{2r} = 22/7 $$

where `r + \delta` is the major axis, `r` is the minor axis and `C(r,r+\delta)` is the circumference of the ellipse. Substituting the expression for the circumference, $$ 4(r+\delta) \int_0^{\pi/2} \sqrt { 1 - \left(1-\frac{r}{(r+\delta)^2}\right)\sin^2 \theta } d \theta = 2 r \frac{22}{7}$$

If we set `r=1` and solve it turns out that only a very minor deformation is required and `\delta = 0.0008`. You can verify this at Wolfram Alpha.

I wanted to make some art based on the shape of the this ellipse, but a deformation of 0.08% is not perceptible. So I came up with a slightly different approach to how I define the original circumference-to-diameter ratio.

Instead of treating the diameter as `r` and using `r + \delta` as the major axis, I now define the diameter as twice the average radius, or `2r + \delta`. This means that the equation to solve is $$ \frac{C(r,r+\delta)}{2r+\delta} = 22/7 $$

As before, setting `r=1` and substituting the expression for the circumference of an ellipse, we get $$ 4(1+\delta) \int_0^{\pi/2} \sqrt { 1 - \left(1-\frac{1}{(1+\delta)^2}\right)\sin^2 \theta } d \theta = (2+\delta) \frac{22}{7}$$

and solving this for `\delta` find $$ \delta = 0.083599769... $$

You can verify this at Wolfram Alpha.

This is a more useable approach since an 8% warping of a circle can be easily perceived.

Pi Approximation Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The ratio of the circumference of a circle, `C(r)`, to its dimameter, `2r`, is `\pi`. If we warp the circle by 8%, the corresponding ratio, if we use twice the average radius as the diameter, is 22/7. This deformation can be easily identified.

Below is matrix of perfect circles along side the 8% deformed circles.

Pi Approximation Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A matrix of perfect circles and ones which have been stretched by 8% along one axis and then randomly rotated. The deformed circles embody the `\pi` approximation of 22/7.

The art posters are based on a packing of these deformed circles.

Pi Approximation Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Warped circles, packed.
Pi Approximation Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Even more warped circles, packed.

By superimposing perfect circles on the warped circles, fun patterns appear.

Pi Approximation Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Superposition of perfect and warped circles, packed.

perfect vs approximate packing

If you pack perfect circles perfectly, the area occupied by the circles is `\pi/4 = 78.5%`.

What is the area occupied by perfect packing of warped and randomly rotated (like in the posters) circles?

color scheme

To motivate choice of colors, I chose images with a 1970's feel.

Pi Approximation Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Images used for color schemes. The colors of each image were grouped into clusters—8 for the first two images and 6 for the third—to obtain proportions of representative colors.

Using my color summarizer, I analyzed each image for its representative colors. Using these colors and their proportions, I colored the perfect and warped circles.

Pi Approximation Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Packed warped circles colored in proportion to color schemes derived from the images above.

For each poster of these color schemes, two poster versions are available. In one, the perfect cirlces are shown with warped circles as a clip mask. In the other, warped circles are shown, clipped by perfect circles.

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.

Small hours
of
the world and me.

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).