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
Here we are now at the middle of the fourth large part of this talk.Pepe Deluxeget nowheremore quotes

e: curious


The Outbreak Poems — artistic emissions in a pandemic


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.

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


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

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

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

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

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

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

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

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

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

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)

VIEW ALL

news + thoughts

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.

Poster Design Guidelines

Wed 15-07-2020

Clear, concise, legible and compelling.

The PDF template is a poster about making posters. It provides design, typography and data visualiation tips with minimum fuss. Follow its advice until you have developed enough design sobriety and experience to know when to go your own way.

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

The SEIRS model for infectious disease dynamics

Thu 18-06-2020

Realistic models of epidemics account for latency, loss of immunity, births and deaths.

We continue with our discussion about epidemic models and show how births, deaths and loss of immunity can create epidemic waves—a periodic fluctuation in the fraction of population that is infected.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: The SEIRS model for infectious disease dynamics. (read)

This column has an interactive supplemental component (download code) that allows you to explore epidemic waves and introduces the idea of the phase plane, a compact way to understand the evolution of an epidemic over its entire course.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: The SEIRS model for infectious disease dynamics. (Interactive supplemental materials)

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.

Background reading

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

Gene Machines

Fri 05-06-2020

Shifting soundscapes, textures and rhythmic loops produced by laboratory machines.

In commemoration of the 20th anniversary of Canada's Michael Smith Genome Sciences Centre, Segue was commissioned to create an original composition based on audio recordings from the GSC's laboratory equipment, robots and computers—to make “music” from the noise they produce.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Gene Machines by Segue. Now available on vinyl.