Thoughts rearrange, familiar now strange.break flowersmore quotes

# constellations: exciting

The Outbreak Poems — artistic emissions in a pandemic

# visualization + design

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.
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 2017 Art Posters - Star charts and extinct animals and plants

2019 $\pi$ has hundreds of digits, hundreds of languages and a special kids' edition.
2018 $\pi$ day
2017 $\pi$ day
2016 $\pi$ approximation day
2016 $\pi$ day
2015 $\pi$ day
2014 $\pi$ approx day
2014 $\pi$ day
2013 $\pi$ day
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.

All art posters are available for purchase.
I take custom requests.

Caelum non animum mutant qui trans mare currunt.
—Horace

This year: creatures that don't exist, but once did, in the skies.

This year's $\pi$ day song is Exploration by Karminsky Experience Inc. Why? Because "you never know what you'll find on an exploration".

If you like space, you'll love my the 12,000 billion light-year map of clusters, superclusters and voids. Find the biggest nothings in Boötes and Eridanus.

## create myths and contribute!

Want to contribute to the mythology behind the constellations in the $\pi$ in the sky? Many already have a story, but others still need one. Please submit your stories!

If you follow my projects, you know that a big part of the final piece is the story and method behind its creation.

I'm not content to merely show what I have made. By talking about the process, its messiness, failures and successes, I'm hopeful that you'll take away something that will inspire you and help you be more creative and productive in your pursuits.

This year's project has a lot of components and is probably my most ambitious yet. It is a mixture of math and storytelling through patterns and mythologies.

As usual, finding patterns and stories in $\pi$ is an ironic pursuit and irony is the best of all wits.

## the digits of $\pi$ as a star catalogue

The digits of $\pi$ are parsed from the start in blocks of 12. The digits in each block are interpreted as the $(x,y,z)$ coordinates of the star, with only 3 digits used for the $z$ coordinate. The last digit is the absolute magnitude of the star ($M_{abs}$).

314159265358
----++++---+
x   y   z  Mabs

By parsing the first 12 million digits, you get a million stars. Each star's apparent magnitude, ($M_{app}$) is calculated from its absolute magnitude and its longitude and latitude in the sky is calculated using conversion from Cartesian to spherical coordinates.

#    i digits        name      x      y     z      long     lat         d  Mabs  Mapp
0 314159265358     a  -1859    926    35  145.339  -38.384  2077.157  3.00 14.59
1 979323846264     b   4793  -2616   126  -38.404   39.555  5461.884 -1.00 12.69
2 338327950288     c  -1617  -2205  -472 -110.162  -32.164  2774.797  3.00 15.22
...
999997 420478142596 cexhl   -796   2814  -241   97.939  -14.471  2934.330  1.00 13.34
999998 278256213419 cexhm  -2218    621  -159  156.900  -46.719  2308.776  4.00 15.82
999999 453839371943 cexhn   -462  -1063  -306  -95.924  -26.937  1198.770 -2.00  8.39

The coordinates are centered on zero by subtracting the average coordinate (4999 for $x$ and $y$ and 499 for $z$) from the sequence of digits.

3141    5926     535
-4999.5  4999.5   499.5
----    ----     ---
x -1859  y  926   z  35

### apparent brightness

The star's absolute magnitude is in the range -5 (brightest) to 5 (dimmest). The apparent magnitude is given by $$M_{app} = M_{abs} + 5 \left( \log_{10} d - 1 \right)$$

So for the first star, whose distance from the origin (the location of the observer planet), $$M_{app} = 3 + 5 \left ( log_{10} 2077.157 - 1 \right) = 3 + 5 \times 2.31 = 14.59$$

For each difference in one apparent magnitude, the change in brightness is a factor of $100^{1/5} = 2.5$.

## exploring projections

The stars' position in the universe $(x,y,z)$ are projected onto the unit sphere to calculate their longitude $-180 .. 180$ and latitude $-90 .. 90$ coordinates.

Once this is done the next step is to figure out how to project the unit sphere onto the page.

The plate carrée, azimuthal equidistant, Mollweide and Hammer projections of the globe. Source: Wikipedia. (list of projections)

There is a huge number of topographical projections to choose from. In star charts, some common ones are plate Carrée and azimuthal equidistant projections.

The Carrée simply maps lines of latitude and longitude to equally spaced lines. The azimuthal equidistant projection is more complicated and has the property that all points on the map are at proportionately correct distances from the center point. The flag of the United Nations uses this kind of projection.

I also wanted to explore the Mollweide projection because this is the one used in the famous background microwave background radiation image. This projection has some artefacts around the edges so instead I used the very similar Hammer/Aitoff projection, which has less distortion at the outer meridians.

The discussion of whether to use Mollweide or Hammer is a hot topic of debate at xkcd. Maybe one day I'll make a Mollweide map too.

At this point it would be criminal of me not to acknowledge Craig DeForest's PDL::Transform::Cartography module. I had a few questions about syntax and he wrote back to me within a few hours of my query.

To be honest, I haven’t used t_vertical since I got t_perspective online (some 12 or so years ago). I'll have a look at it tonight and try to get you a useful answer. Stand by a couple of hours—it’s putting-down-kids-to-bed time.
—Craig DeForest

That is the most awesome support I have ever received!

## a cube of stars

To illustrate how an arrangement of stars looks in each projection, let's start with a cube of stars.

A cube of stars. (zoom)

For this, I created a catalog of stars that fill the cube centered on (0,0,0) and having an edge length of 10,000. This size of cube represents the limits of the coordintaes in the catalog based on the digits of $\pi$. I arbitrarily set the absolute magnitude of each star to -8 and use the same star size encoding on here as in the final chart.

Stars close to the "galactic plane" ($z$ coordinate close to zero) are tinted red. As for the final charts, the observer planet is rotated so that this plane approximates how the Milky Way looks in actual charts.

A 3-dimensional grid of stars in a plate carrée projection. Stars falling close to the galactic plane are tinted red. (zoom)
A 3-dimensional grid of stars in a Hammer/Aitoff projection. Stars falling close to the galactic plane are tinted red. (zoom)

In the azimuthal projection, I decided to show a little bit of the opposite hemisphere. The north hemisphere map range is $[-10,90]$ and the south hemisphere range is $[-90,10]$. This provides some continuity around the edges. The bright white circle near the edge of the hemispheres represents the celestial equator.

A 3-dimensional grid of stars in an azimuthal equidistant projection. North hemisphere. Stars falling close to the galactic plane are tinted red. (zoom)
A 3-dimensional grid of stars in an azimuthal equidistant projection. South hemisphere. Stars falling close to the galactic plane are tinted red. (zoom)

It's interesting to see where the stars that fall on the faces of the cube wind up on the chart. These represent the furthest reaches of this synthetic universe.

Stars falling on the edges of a cube in a plate carrée projection. Stars falling close to the galactic plane are tinted red. (zoom)
Stars falling on the edges of a cube in a Hammer/Aitoff projection. Stars falling close to the galactic plane are tinted red. (zoom)
Stars falling on the edges of a cube in an azimuthal equidistant projection. North hemisphere. Stars falling close to the galactic plane are tinted red. (zoom)
Stars falling on the edges of a cube in an azimuthal equidistant projection. South hemisphere. Stars falling close to the galactic plane are tinted red. (zoom)

## what does randomness look like?

Let's look at what a random distribution of stars looks like on the charts. The final $\pi$ star charts draw 40,000 stars from the first 12,000,000 digits, so let's create a catalog of 40,000 stars in which the location of the star is uniformly randomly distributed within a cube. The stars will have random absolute magnitude in the range -5 to 5.

This is roughly what we can expect from $\pi$, since the number is likely normal.

These images are best viewed when zoomed in—go ahead, click on them.

40,000 randomly placed stars within a cube in a plate carrée projection. Stars falling close to the galactic plane are tinted yellow. (zoom)
40,000 randomly placed stars within a cube in a Hammer/Aitoff projection. Stars falling close to the galactic plane are tinted yellow. (zoom)
40,000 randomly placed stars within a cube in an azimuthal equidistant projection. North hemisphere. Stars falling close to the galactic plane are tinted yellow. (zoom)
40,000 randomly placed stars within a cube in an azimuthal equidistant projection. South hemisphere. Stars falling close to the galactic plane are tinted yellow. (zoom)

If we fill a cube (or a sphere) with digits in this way, we're not going to wind up with anything particularly intersting. We'll see randomness—and that's ok!— but I wanted the chart to more resemble an actual sky chart.

## creating anisotropy

If you were paying particular attention, you may be wondering why the $z$ coordinate was determined by only 3 digits.

Because the digits of $\pi$ are without pattern (the digit is thought to be normal, meaning that in any subsequence all the digits have the same chance of appearing, a universe created from its digits is going to be isotropic. In other words, it will look the same in all directions—uniformly random!

I knew I wanted the chart to have a look similar to the charts of our sky—with a bright band of stars, which in our sky represent the stars within the plane of the Milky Way.

By using only 3 digits for the $z$ coordinate and 4 digits for $x$ and $y$, the universe of stars doesn't fill a cube but a flat 3-d rectangle. It's 10 times thinner than it is wide.

By rotating the observer planet, I was able to match the location of the band in my star chart to roughly that of the Milky Way in standard charts.

A basic render of the $\pi$ star chart in plate carrée projection, with focus on the band of stars in the direction of the plane of the universe. (zoom)
A basic render of the $\pi$ star chart in Hammer/Aitoff projection, with focus on the band of stars in the direction of the plane of the universe (zoom)
A basic render of the $\pi$ star chart in Hammer/Aitoff projection, with focus on the band of stars in the direction of the plane of the universe (zoom)

Although the charts only show 40,000 stars (up to apparent magnitude of about –8), more are used to determine the glow of the bands shown in the charts above. To do this, I divided the chart into a 240 × 160 grid and counted the number of stars in each grid. Then, the counts were smoothed and 25, 50, 75, 90, 95 and 99 percentile contours were calculated to provide layering in the bands.

## constellations

I knew from the beginning that the constellations would play a big role in the chart. If we think of $\pi$ as a star catalogue, then it makes sense that it doesn't include any information about constellations, since these change with time and position of the observer.

It is up to us (me) to look up and figure out patterns.

But how to name the constellations? This plagued me for a long time.

Famous mathematicians? No, that's exactly what people would expect.

Mathematical formulae that use $\pi$? Fun and each equation has a story, but I didn't want it to get too arcane.

Projecting names of places on the Earth on the corresponding part of the sky? This initially sounded like a great way to sample strange and interesting names and set up a double projection on the chart—up from the Earth and down from space.

Below is an early attempt at drawing some kind of patterns in the sky. The shapes weren't motivated by anything in particular.

An early attempt at making constellations. Stars that are part of the constellation are used to tesselate the map. The tesselation polygons are then joined to create boundaries. (zoom)

I wasn't very happy with just drawing random shapes. I also wasn't very happy with the boundaries of the constellations being created from a mindless tesselation. Real constellation boundaries usually fall parallel to longitude and latitude lines and the tesselated boundaries didn't look anything like that.

Then I had a better idea.

### populating the sky with critters and veggies

I was going to populate the sky with extinct plants and animals.

I wanted the constellations to be an homage to the wonderful way Nature has a way of arranging molecules into living things, in part a poetic statement about the passage of time and life and in part a source of mythology for the chart.

After all, most of us have personalities. It's reasonable to expect that these animals did too—behaviour is the fun part of life.

I was quickly met with giant lists of extinct species. Independently, I discovered that if you add "list" to any Google search query you'll be kidnapped by clickbait and listicles, of the worst kind: "10 reasons why your cat wants you extinct". Just kidding. Or not.

It took me a good week to work through the lists and collect animals that seemed to have interesting stories. There are 88 constellations in our sky and I managed to create a new set of 80. Finding patterns in randomly placed dots on the screen is partly fun and slightly frustrating. Oh, look, that definitely looks like a Dodo. Wait. Now this here definitely looks like a Dodo. I was seeing Dodos everywhere.

I hunted for constellations by moving around shapes of animals and keying off bright stars. (zoom)

Once I had some clipart of the species on the artboard, I started looking for patterns. I labeled stars with short readable words from the dictionary (e.g. 4-5 letters long with 2 vowels). In the catalogue they're mindlessly coded from a to cexhn, which are hard to type. Then, I went to work defining graph edges that would be the constellations.

Each star was assigned a readable label that I used for the definition. (zoom)

Once I had them drawn, I translated the readable words into the original star labels to have a constellation file like this:

# a winding constellation
rodhocetus:
bbiam kefp bxisk bvzam camyi xzhs

# several edges
pterodactyl:
soew brxrr bjass bpftr baelv brnhi kxfu jjco
baelv bkpew

# the trailing . indicates a closed shape
traversia:
puib fywb fcnw .

After finding some constellations, I was showing my work to Jake Lever, a colleague who is often an excellent inspiration for ideas. We've co-authored some Points of Significance columns, so I know Jake is really sharp.

I was complaining to Jake that I was having trouble with the Polygon clipper library, which sometimes wasn't merging polygons that shared an edge. I wanted to automate as much of the process as possible, I said, and didn't want to draw the boundaries of the constellations by hand.

As soon as I said this, I thought... but I really should do them properly. I was using automation as a way to not spend making the sky charts even more excellent.

Rough was the day when I realized I had to draw the boundaries by hand. (zoom)

The boundaries actually didn't take that long to draw. Perhaps 20 minutes of making unions of boxes in Illustrator. But then I had to get the position of those shapes back into my star chart drawing code so that I could use it for other projections. Up to now, I was doing all the work in the plate carrée projection. This meant that I had to go back to the code and make everything less of a complete kludge. Damn it, I'm a prototyper not a software developer!

In the end, I think this step was not only worth it but necessary and made the chart appear more authentic.

A basic render of the $\pi$ star chart in plate carrée projection, with focus on the boundaries between constellations. (zoom)
A basic render of the $\pi$ star chart in Hammer/Aitoff projection, with focus on the boundaries between constellations. (zoom)
A basic render of the $\pi$ star chart in Hammer/Aitoff projection, with focus on the boundaries between constellations. (zoom)

Most stars don't have memorable names. Not everyone can be a Betelgeuse or Rigel.

To help identify stars, they are labeled by their constellation (e.g. Orion) and their relative brightness within that constellation compared to other stars. Because Betelgeuse is the brightest it is first and given the name α Orionis. Rigel is second brightest, so it is β Orionis. The third brightest star is γ, and so on.

I added a layer of labels. All stars brighter than apparent magnitude 4.5 have labels along with any stars that are used to draw the shape of the constellation shape, if they're dimmer. The labels range from α to ω.

A basic render of the $\pi$ star chart in plate carrée projection, with focus on the relative magnitude labels for the brightest stars within a constellation. (zoom)

## putting it together

The individual components of the chart were generated in SVG, which was then imported into Illustrator. Below is a look at the layer organization.

Layer organization in Illustrator. (zoom)

I am grateful to the music of Hooverphonic and Chicane to sustain long hours of coding, finding shapes of animals and imagining their stories. And, as always, Galileo coffee which sustains our entire genome center.

There's not just truth in coffee, but life.

# 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.

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.

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.

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.

Gene Machines by Segue. Now available on vinyl.

# Virus Mutations Reveal How COVID-19 Really Spread

Mon 01-06-2020

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.

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.

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

Tue 16-06-2020

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.

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 $R_0$.

Nature Methods Points of Significance column: Modeling infectious epidemics. (read)

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.

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.

Tears decline
the