Love itself became the object of her love.count sadnessesmore quotes

# piet mondrian: exciting

Scientific graphical abstracts — design guidelines

# visualization + design

81 digits of $\pi$ as a forest of trees: standard, bat cave and underwater editions. ( BUY ARTWORK )
The 2021 Pi Day art celebrates the digits of $\pi$ with a forest! Visit the bat cave and underwater ecosystems for the full experience.

# $\pi$ Day 2015 Art Posters

2021 $\pi$ reminds us that good things grow for those who wait.' edition.
2019 $\pi$ has hundreds of digits, hundreds of languages and a special kids' edition.
2018 $\pi$ day stitches street maps into new destinations.
2017 $\pi$ day imagines the sky in a new way.

2016 $\pi$ approximation day wonders what would happen if about right was right.
2016 $\pi$ day sees digits really fall for each other.
2015 $\pi$ day maps transcendentally.
2014 $\pi$ approx day spirals into roughness.

2014 $\pi$ day hypnotizes you into looking.
2014 $\pi$ day
2013 $\pi$ day is where it started
Circular $\pi$ art and other distractions

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.

Most of the art is available for purchase as framed prints and, yes, even pillows. Sleep's never been more important — I take custom requests.

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.

Representing a number using a tree map. Each digit of the number is used to successively divide a shape, such as a square. (zoom)

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.

At each level of the tree map, more digits are encoded. Shown here are tree maps for $pi$ for the first 6 levels of division. (zoom)

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).

At each level of the tree map, more digits are encoded. Shown here are tree maps for $pi$ for the first 6 levels of division. (zoom)

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 $i = 1 .. 6$.

$PI PHI e i n_i N_i n_i N_i n_i N_i 1 1 1 1 1 1 1 2 4 5 2 3 3 4 3 15 20 9 12 19 23 4 98 118 59 71 96 119 5 548 666 330 401 574 693 6 2962 3628 1857 2258 3162 3855 7 16616 20244 10041 12299 17541 21396 8 91225 111469 9 500861 612330$

## Dividing the map

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$(0.24/0.14 split). The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom) Using a non-uniform multipler is one way to embed another number in the art. When a multiplier like$phi$is used, divisions at the top levels create very large rectangles. To attenuate this, the effect of the multiplier can be weighted by the level. Regardless of what multiplier is used, the first level is always uniformly divided. Division at subsequent levels incorporates more of the multiplier effect. The orientation of the division can be uniform (same for a layer and alternating across layers), alternating (alternating across and within a layer) or random. This modification has an effect only if the divisions are not uniform. The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom) ## Adjusting line thickness To emphasize the layers, a different line thickness can be used. When lines are drawn progressively thinner with each layer, detail is controlled and the map has more texture. When all lines have the same thickness, it is harder to distinguish levels. The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom) You could see this as a challenge! Below I show the treemaps for$pi$,$phi$and$e$with and without stroke modulation. The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom) When displayed at a low resolution (the image below is 620 pixels across), shapes at higher levels appear darker because the distance between the lines within is close to (or smaller) than a pixel. By matching the line thickness to the image resolution, you can control how dark the smallest divisions appear. The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom) ## Adding color Adding color can make things better, or worse. Dropping color randomly, without respect for the level structure of the treemap, creates a mess. We can rescue things by increasing the probability that a given rectangle will be made transparent—this will allow the color of the rectangle below to show through. Additionally, by drawing the layers in increasing order, smaller rectangles are drawn on top of bigger ones, giving a sense of recursive subdivision. The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom) Because the color is assigned randomly, various instances of the treemap can be made. The maps below have the same proportion of colors and transparency (same as the first image in second row in the figure above) and vary only by the random seed to pick colors. Different instances of 5 level$pi$treemaps. The proportion of transparent, white, yellow, red and blue shapes is 20:1:1:1:1. (zoom) ## Coloring using adjacency graph The color assignments above were random. For each shape the probability of choosing a given color (transparent, white, yellow, red, blue) was the same. Color choice for a shape can also be influenced by the color of neighbouring shapes. To do this, we need to create a graph that captures the adjacency relationship between all the shapes at each level. Below I show the first 4 levels of the$pi$treemap and their adjacency graphs. In each graph, the node corresponds to a shape and an edge between nodes indicates that the shapes share a part of their edge. Shapes that touch only at a corner are not considered adjacent. Different instances of 5 level$pi$treemaps. The proportion of transparent, white, yellow, red and blue shapes is 20:1:1:1:1. (zoom) One way in which the graphs can be used is to attempt to color each layer using at most 4 colors. The 4 color theorem tells us that only 4 unique colors are required to color maps such as these in a way that no two neighbouring shapes have the same color. It turns out that the full algorithm of coloring a map with only 4 colors is complicated, but reasonably simple options exist.. For the maps here, I used the DSATUR (maximum degree of saturation) approach. Different instances of 5 level$pi$treemaps. The proportion of transparent, white, yellow, red and blue shapes is 20:1:1:1:1. (zoom) The DSATUR algorithm works well, but does not guarantee a 4-color solution. It performs no backtracking. If you look carefully, one of the rectangles in the 4th layer (top right quadrant in the graph) required a 5th color (shown black). # VIEW ALL # news + thoughts # The COVID charts — hospitalization rates Tue 25-01-2022 As part of the COVID Charts series, I fix a muddled and storyless graphic tweeted by Adrian Dix, Canada's Health Minister. I show you how to fix color schemes to make them colorblind-accessible and effective in revealing patters, how to reduce redundancy in labels (a key but overlooked part of many visualizations) and how to extract a story out of a table to frame the narrative. Clear titles introduce the graphic, which starts with informative and non-obvious observations of the relationship between age, number of comorbidities, vaccination status and hospitalization rates. Supporting the story is a tidy table that gives you detailed statistics for each demographic. (more) # Music for the Moon: Flunk's 'Down Here / Moon Above' Sat 29-05-2021 The Sanctuary Project is a Lunar vault of science and art. It includes two fully sequenced human genomes, sequenced and assembled by us at Canada's Michael Smith Genome Sciences Centre. The first disc includes a song composed by Flunk for the (eventual) trip to the Moon. But how do you send sound to space? I describe the inspiration, process and art behind the work. The song 'Down Here / Moon Above' from Flunk's new album History of Everything Ever is our song for space. It appears on the Sanctuary genome discs, which aim to send two fully sequenced human genomes to the Moon. (more) # Happy 2021$\pi$Day—A forest of digits Sun 14-03-2021 Celebrate$\pi$Day (March 14th) and finally see the digits through the forest. The 26th tree in the digit forest of$\pi$. Why is there a flower on the ground?. (details) This year is full of botanical whimsy. A Lindenmayer system forest – deterministic but always changing. Feel free to stop and pick the flowers from the ground. The first 46 digits of$\pi$in 8 trees. There are so many more. (details) And things can get crazy in the forest. A forest of the digits of '\pi$, 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.

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.

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.

Graphical Abstract Design Guidelines — Clear, concise, legible and compelling.