resources
visualizations
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lunch break
Distractions and amusements, with a sandwich and coffee.
visualization + design
They serve as the form for The Outbreak Poems.
The art of Pi (`\pi`), Phi (`\phi`) and `e`
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.
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.
The original images were generated using the 10-color Brewer paired qualitative palette, which was later modified as shown below.
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.
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The image below shows how this representation of `\pi` compares to that of `\phi` and `e`.
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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.
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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.
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`.
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.
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spiral art of `\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.
I have use the Archimedean spiral to make art for `\pi` approximation day
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news + thoughts
The SEIRS model for infectious disease dynamics
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.
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.
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
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.
Virus Mutations Reveal How COVID-19 Really Spread
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.
Cover of Nature Cancer April 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.
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
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.
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`.
This column has an interactive supplemental component (download code) that allows you to explore how the model curves change with parameters such as infectious period, basic reproduction number and vaccination level.
Bjørnstad, O.N., Shea, K., Krzywinski, M. & Altman, N. (2020) Points of significance: Modeling infectious epidemics. Nature Methods 17:455–456.
The Outbreak Poems
I'm writing poetry daily to put my feelings into words more often during the COVID-19 outbreak.
Tears decline the plural of sad.
Souls look out from dark eye windows.