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Distractions and amusements, with a sandwich and coffee.

Trance opera—Spente le Stelle
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They serve as the form for The Outbreak Poems.

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.

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.

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.

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).

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

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).

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.

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.

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

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.

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.

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.

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.

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.

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).

*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.

*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.

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

*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.

*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.

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.

*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.