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
Twenty — minutes — maybe — more.Naomichoose four wordsmore quotes

piet mondrian: fun


Scientific graphical abstracts — design guidelines


visualization + design

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.
Music video of the “Transcendental Tree Map” Max Cooper's Yearning for the Infinite album. 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.
Tau Day tree map animation of 8,909 digits of `\tau = 2 \pi` created with 40,015 lines. The video is 6:28 minutes long.

`\pi` Day 2015 Art Posters


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2019 `\pi` has hundreds of digits, hundreds of languages and a special kids' edition.

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2018 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2017 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` approximation day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` approx day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 `\pi` day

Pi Day 2015 Art Posters
 / 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.

Not a circle in sight in the 2015 `\pi` day art. Try to figure out how up to 612,330 digits are encoded before reading about the method. `\pi`'s transcendental friends `\phi` and `e` are there too—golden and natural. Get it?

This year's `\pi` day is particularly special. The digits of time specify a precise time if the date is encoded in North American day-month-year convention: 3-14-15 9:26:53.

The art has been featured in Ana Swanson's Wonkblog article at the Washington Post—10 Stunning Images Show The Beauty Hidden in `\pi`.

We begin with a square and progressively divide it. At each stage, the digit in `pi` is used to determine how many lines are used in the division. The thickness of the lines used for the divisions can be attenuated for higher levels to give the treemap some texture.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Representing a number using a tree map. Each digit of the number is used to successively divide a shape, such as a square. (zoom)

This method of encoding data is known as treemapping. Typically, it is used to encode hierarchical information, such as hard disk spac usage, where the divisions correspond to the total size of files within directories.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
At each level of the tree map, more digits are encoded. Shown here are tree maps for `pi` for the first 6 levels of division. (zoom)

This kind of treemap can be made from any number. Below I show 6 level maps for `pi`, `phi` (Golden ratio) and `e` (base of natural logarithm).


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
At each level of the tree map, more digits are encoded. Shown here are tree maps for `pi` for the first 6 levels of division. (zoom)

The number of digits per level, `n_i` and total digits, `N_i` in the tree map for `pi`, `phi` and `e` is shown below for levels `i = 1 .. 6`.

           PI             PHI              e
i     n_i    N_i      n_i    N_i      n_i    N_i
1       1      1        1      1        1      1
2       4      5        2      3        3      4
3      15     20        9     12       19     23
4      98    118       59     71       96    119
5     548    666      330    401      574    693
6    2962   3628     1857   2258     3162   3855
7   16616  20244    10041  12299    17541  21396
8   91225 111469
9  500861 612330

Dividing the map

In all the treemaps above, the divisions were made uniformly for each rectangle. With uniform division, the lines that divide a shape are evenly spaced. With randomized division, the placement of lines is randomized, while still ensuring that lines do not coincide.

A multiplier, such as `phi` (Golden Ratio), can be used to control the division. In this case, the first division is made at 1/`phi` (0.62/0.38 split) and the remaining rectangle (0.38) is further divided at `/`phi` (0.24/0.14 split).


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom)

Using a non-uniform multipler is one way to embed another number in the art.

When a multiplier like `phi` is used, divisions at the top levels create very large rectangles. To attenuate this, the effect of the multiplier can be weighted by the level. Regardless of what multiplier is used, the first level is always uniformly divided. Division at subsequent levels incorporates more of the multiplier effect.

The orientation of the division can be uniform (same for a layer and alternating across layers), alternating (alternating across and within a layer) or random. This modification has an effect only if the divisions are not uniform.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom)

Adjusting line thickness

To emphasize the layers, a different line thickness can be used. When lines are drawn progressively thinner with each layer, detail is controlled and the map has more texture.

When all lines have the same thickness, it is harder to distinguish levels.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom)

You could see this as a challenge! Below I show the treemaps for `pi`, `phi` and `e` with and without stroke modulation.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom)

When displayed at a low resolution (the image below is 620 pixels across), shapes at higher levels appear darker because the distance between the lines within is close to (or smaller) than a pixel. By matching the line thickness to the image resolution, you can control how dark the smallest divisions appear.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom)

Adding color

Adding color can make things better, or worse. Dropping color randomly, without respect for the level structure of the treemap, creates a mess.

We can rescue things by increasing the probability that a given rectangle will be made transparent—this will allow the color of the rectangle below to show through. Additionally, by drawing the layers in increasing order, smaller rectangles are drawn on top of bigger ones, giving a sense of recursive subdivision.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom)

Because the color is assigned randomly, various instances of the treemap can be made. The maps below have the same proportion of colors and transparency (same as the first image in second row in the figure above) and vary only by the random seed to pick colors.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Different instances of 5 level `pi` treemaps. The proportion of transparent, white, yellow, red and blue shapes is 20:1:1:1:1. (zoom)

Coloring using adjacency graph

The color assignments above were random. For each shape the probability of choosing a given color (transparent, white, yellow, red, blue) was the same.

Color choice for a shape can also be influenced by the color of neighbouring shapes. To do this, we need to create a graph that captures the adjacency relationship between all the shapes at each level. Below I show the first 4 levels of the `pi` treemap and their adjacency graphs. In each graph, the node corresponds to a shape and an edge between nodes indicates that the shapes share a part of their edge. Shapes that touch only at a corner are not considered adjacent.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Different instances of 5 level `pi` treemaps. The proportion of transparent, white, yellow, red and blue shapes is 20:1:1:1:1. (zoom)

One way in which the graphs can be used is to attempt to color each layer using at most 4 colors. The 4 color theorem tells us that only 4 unique colors are required to color maps such as these in a way that no two neighbouring shapes have the same color.

It turns out that the full algorithm of coloring a map with only 4 colors is complicated, but reasonably simple options exist.. For the maps here, I used the DSATUR (maximum degree of saturation) approach.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Different instances of 5 level `pi` treemaps. The proportion of transparent, white, yellow, red and blue shapes is 20:1:1:1:1. (zoom)

The DSATUR algorithm works well, but does not guarantee a 4-color solution. It performs no backtracking. If you look carefully, one of the rectangles in the 4th layer (top right quadrant in the graph) required a 5th color (shown black).

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news + thoughts

Graphical Abstract Design Guidelines

Fri 13-11-2020

Clear, concise, legible and compelling.

Making a scientific graphical abstract? Refer to my practical design guidelines and redesign examples to improve organization, design and clarity of your graphical abstracts.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Graphical Abstract Design Guidelines — Clear, concise, legible and compelling.

"This data might give you a migrane"

Tue 06-10-2020

An in-depth look at my process of reacting to a bad figure — how I design a poster and tell data stories.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A poster of high BMI and obesity prevalence for 185 countries.

He said, he said — a word analysis of the 2020 Presidential Debates

Thu 01-10-2020

Building on the method I used to analyze the 2008, 2012 and 2016 U.S. Presidential and Vice Presidential debates, I explore word usagein the 2020 Debates between Donald Trump and Joe Biden.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Analysis of word usage by parts of speech for Trump and Biden reveals insight into each candidate.

Points of Significance celebrates 50th column

Mon 24-08-2020

We are celebrating the publication of our 50th column!

To all our coauthors — thank you and see you in the next column!

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance: Celebrating 50 columns of clear explanations of statistics. (read)

Uncertainty and the management of epidemics

Mon 24-08-2020

When modelling epidemics, some uncertainties matter more than others.

Public health policy is always hampered by uncertainty. During a novel outbreak, nearly everything will be uncertain: the mode of transmission, the duration and population variability of latency, infection and protective immunity and, critically, whether the outbreak will fade out or turn into a major epidemic.

The uncertainty may be structural (which model?), parametric (what is `R_0`?), and/or operational (how well do masks work?).

This month, we continue our exploration of epidemiological models and look at how uncertainty affects forecasts of disease dynamics and optimization of intervention strategies.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Uncertainty and the management of epidemics. (read)

We show how the impact of the uncertainty on any choice in strategy can be expressed using the Expected Value of Perfect Information (EVPI), which is the potential improvement in outcomes that could be obtained if the uncertainty is resolved before making a decision on the intervention strategy. In other words, by how much could we potentially increase effectiveness of our choice (e.g. lowering total disease burden) if we knew which model best reflects reality?

This column has an interactive supplemental component (download code) that allows you to explore the impact of uncertainty in `R_0` and immunity duration on timing and size of epidemic waves and the total burden of the outbreak and calculate EVPI for various outbreak models and scenarios.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Uncertainty and the management of epidemics. (Interactive supplemental materials)

Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: Uncertainty and the management of epidemics. Nature Methods 17.

Background reading

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

Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: The SEIRS model for infectious disease dynamics. Nature Methods 17:557–558.

Cover of Nature Genetics August 2020

Mon 03-08-2020

Our design on the cover of Nature Genetics's August 2020 issue is “Dichotomy of Chromatin in Color” . Thanks to Dr. Andy Mungall for suggesting this terrific title.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Dichotomy of Chromatin in Color. Nature Genetics, August 2020 issue. (read more)

The cover design accompanies our report in the issue Gagliardi, A., Porter, V.L., Zong, Z. et al. (2020) Analysis of Ugandan cervical carcinomas identifies human papillomavirus clade–specific epigenome and transcriptome landscapes. Nature Genetics 52:800–810.