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
I'm not real and I deny I won't heal unless I cry.Cocteau Twinslet it gomore quotes

circles: beautiful


Scientific graphical abstracts — design guidelines


visualization + design


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
81 digits of `\pi` as a forest of trees: standard, bat cave and underwater editions. ( BUY ARTWORK )
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The 2021 Pi Day art celebrates the digits of `\pi` with a forest! Visit the bat cave and underwater ecosystems for the full experience.

The art of Pi (`\pi`), Phi (`\phi`) and `e`


Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2021 `\pi` reminds us that good things grow for those who wait.' edition.

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

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2018 `\pi` day stitches street maps into new destinations.

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2017 `\pi` day imagines the sky in a new way.


Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` approximation day wonders what would happen if about right was right.

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` day sees digits really fall for each other.

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

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` approx day spirals into roughness.


Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day hypnotizes you into looking.

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

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 `\pi` day is where it started

Pi Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Circular `\pi` art and other distractions

This section contains various art work based on `\pi`, `\phi` and `e` that I created over the years.

Some of the numerical art reveals interesting and unexpected observations. For example, the sequence 999999 in π at digit 762 called the Feynman Point. Or that if you calculate π to 13,099,586 digits you will find love.

`\pi` day art and `\pi` approximation day art is kept separate.

All of the posters are listed in the posters section. Some also appear in the methods section, where I describe how they were made. Most of the circular art was made with Circos.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A path connecting segments traces out the digits of `\pi`. Here the transition for the 6 digits is shown. Concept by Cristian Ilies Vasile. Created with Circos.

Cristian Ilies Vasile had the idea of representing the digits of `\pi` as a path traced by links between successive digits. Each digit is assigned a segment around the circle and a link between segment `i` and `j` corresponds to the appearance of `ij` in `\pi`. For example, the "14" in "3.14..." is drawn as a link between segment 1 and segment 4.

The position of the link on a digit's segment is associated with the position of the digit `\pi`. For example, the "14" link associated with the 2nd digit (1) and the 3rd digit (4) is drawn from position 2 on the 1 segment to position 3 on the 4 segment.

As more digits are added to the path, the image becomes a weaving mandala.

circos art of `\pi`, `\phi` and `e`—transition paths and bubbles

I added to Cristian's representation by showing the number of transitions between digits in a series of concentric circles placed outside the links. This summary representation counts the number of transition links within a region and addresses the question of what kind of digits appear immediately before or after a given digit in `\pi`. The approach is diagrammed below.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The number of transitions to and from a given digit within a window of 10 digits is shown by circles. For a given digit segment (here, 9) each circle indicates the presence of a specific digit appearing before (inner track) or after (after track) the digit. Solid circles are used for the digit that appears most often and if all digits appear equally often, the choice is arbitrary. In some images the order of digits in the inner track is outward. (zoom)

The original images were generated using the 10-color Brewer paired qualitative palette, which was later modified as shown below.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
For added visual impact, I inverted the color palette and added hue shift and vibrance effects.

The bubbles that count the number of links quickly draw attention to regions where specific digit pairs are frequent. In the image for `\pi` below, which shows transitions for the first 1,000 digits, the large bubble on the 9 segment is due to the "999999" sequence at decimal place 762. This is the Feynman point, which I describe below.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Progression and transition for the first 1,000 digits of `\pi`. Created with Circos. (PNG, BUY ARTWORK )

The image below shows how this representation of `\pi` compares to that of `\phi` and `e`.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Progression and transition for the first 1,000 digits of `\pi`, `\phi` and `e`. Created with Circos. (PNG, BUY ARTWORK )

The transition probabilities for each 10 digit bin for the first 2,000 digits of `\pi`, `\phi` and `e` are shown in the image below.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Progression and transition for the first 2,000 digits of `\pi`, `\phi` and `e`. Created with Circos. (PNG, BUY ARTWORK )

Feynman point

This sequence of 6 9's occurs significantly earlier than expected by chance. Because the distribution and sequence of digits of `\pi` is thought to be normal, we can calculate how frequently we should expect a series of 6 identical digits.

For a given digit, the chance that the next 5 digits are the same is 0.00001 (0.1 that the next digit is the same × 0.1 that the second-nex digit is the same × ...). Therefore the chance that a given position the next 5 digits are not the same is 1 - 1/0.00001 = 0.99999. From this, the chance that `k` consecutive digits don't initiate a 6-digit sequence is therefore 0.99999`k`.

If I ask what is `k` for which this value is 0.5, I need to solve 0.99999`k`, which gives `k` = 69,314. Thus, chances are even (50%) that in a 69,000 digit random sequence we'll see a run of 6 idendical digits. This calculation is an approximation.

It's fun to look for words in `\pi`. For example, love appears at 13,099,586th digit.

A tangent into randomness

The digits of `\pi` are, as far as we know, randomly distributed. Art based on its digits therefore as a quality that is influenced by this random distribution. To provide a reference of what such a random pattern looks like, below are 16 random numbers represented in the same way. They're all different, yet strangely the same.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Digit transition paths of sixteen 1,000 digit random numbers. (PNG, BUY ARTWORK )

Circos art of `\pi`—heaps of bubbles

Below are more images by Cristian Ilies Vasile, where dots are used to represent the adjacency between digits. As in the image above, each digit 0-9 is represented by a colored segment. For each digit sequence `ij`, a dot is placed on the `i`th segment at the position of `i` colored by `j`.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
In a digit bubble heap, a digit is represented by a bubble and placed on the segment of its previous neighbour at the index position of the neighbour.

For example, for `\pi` the dot coordinates for the first 7 digits are (segment:position:label) 3:0:1 → 1:1:4 → 4:2:1 → 1:3:5 → 5:4:9 ...

segment position colored_by

3       0        1
1       1        4
4       2        1
1       3        5
5       4        9
9       5        2
2       6        6 

Because there is a large number of digits, the dots stack up near their position to avoid overlapping. The layout of the dots is automated by Circos' text track layout.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Progression and transition for the first 10,000 digits of `\pi`. Created with Circos. (PNG, BUY ARTWORK )

spiral art of `\pi`

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The Archimedean spiral embodies `\pi`.

By mapping the digits onto a red-yellow-blue Brewer palette (0 9) and placing them as circles on an Archimedean spiral a dense and pleasant layout can be obtained.

Why the Archimedean spiral? This spiral is defined as `r = a + b \theta` and has the interesting property that a ray from the origin will intersect the spiral every `2 pi b`. Thus, each spiral can accomodate inscribed circles of radius `\pi b`.

Why the Brewer palette? These color schemes have some very useful perceptual properties and are commonly used to encode quantitative and categorical data.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The digits of π assembled along an Archimedean spiral.
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Calculating (x,y) coordinates for each digit along the Archimedean spiral.
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Distribution of the first 13,689 digits of π. (PNG, BUY ARTWORK )
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Distribution of the first 3,422, 13,689 and 123,201 digits of π. (PNG, BUY ARTWORK )

I have use the Archimedean spiral to make art for `\pi` approximation day

Pi Approximation Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Approximation Day Art Poster | July 22nd is Pi Approximation Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK )

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news + thoughts

Music for the Moon: Flunk's 'Down Here / Moon Above'

Sat 29-05-2021

The Sanctuary Project is a Lunar vault of science and art. It includes two fully sequenced human genomes, sequenced and assembled by us at Canada's Michael Smith Genome Sciences Centre.

The first disc includes a song composed by Flunk for the (eventual) trip to the Moon.

But how do you send sound to space? I describe the inspiration, process and art behind the work.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The song 'Down Here / Moon Above' from Flunk's new album History of Everything Ever is our song for space. It appears on the Sanctuary genome discs, which aim to send two fully sequenced human genomes to the Moon. (more)

Browse the genome discs.

Happy 2021 `\pi` Day—
A forest of digits

Sun 14-03-2021

Celebrate `\pi` Day (March 14th) and finally see the digits through the forest.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The 26th tree in the digit forest of `\pi`. Why is there a flower on the ground?. (details)

This year is full of botanical whimsy. A Lindenmayer system forest – deterministic but always changing. Feel free to stop and pick the flowers from the ground.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The first 46 digits of `\pi` in 8 trees. There are so many more. (details)

And things can get crazy in the forest.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A forest of the digits of '\pi`, by ecosystem. (details)

Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day, 2017 `\pi` Day, 2018 `\pi` Day and 2019 `\pi` Day.

Testing for rare conditions

Sun 30-05-2021

All that glitters is not gold. —W. Shakespeare

The sensitivity and specificity of a test do not necessarily correspond to its error rate. This becomes critically important when testing for a rare condition — a test with 99% sensitivity and specificity has an even chance of being wrong when the condition prevalence is 1%.

We discuss the positive predictive value (PPV) and how practices such as screen can increase it.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Testing for rare conditions. (read)

Altman, N. & Krzywinski, M. (2021) Points of significance: Testing for rare conditions. Nature Methods 18:224–225.

Standardization fallacy

Tue 09-02-2021

We demand rigidly defined areas of doubt and uncertainty! —D. Adams

A popular notion about experiments is that it's good to keep variability in subjects low to limit the influence of confounding factors. This is called standardization.

Unfortunately, although standardization increases power, it can induce unrealistically low variability and lead to results that do not generalize to the population of interest. And, in fact, may be irreproducible.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Standardization fallacy. (read)

Not paying attention to these details and thinking (or hoping) that standardization is always good is the "standardization fallacy". In this column, we look at how standardization can be balanced with heterogenization to avoid this thorny issue.

Voelkl, B., Würbel, H., Krzywinski, M. & Altman, N. (2021) Points of significance: Standardization fallacy. Nature Methods 18:5–6.

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.