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`\pi` Day 2015 Art Posters
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
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).
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.
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.
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
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.
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.
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).
Propensity score weighting
It is not certain that everything is uncertain. —Blaise Pascal
We have already explored how we can mitigate bias caused by confounding variables in observational studies using propensity score (PS) matching (PSM) and propensity score weighting (PSW). However, any statistical model is only as good as its assumptions and, if it is specified incorrectly, it can itself produce biased estimates of the treatment effect.
This month, we explore double robustness, a powerful statistical concept that provides a valuable “safety net” against the risk of an incorrect model. It offers two opportunities, instead of just one, to obtain a valid estimate of the treatment effect — making it possible to draw credible causal inferences from observational data without having to depend on a single set of modeling assumptions.
Kurz, C.F., Krzywinski, M. & Altman, N. (2026) Points of significance: Double Robustness. Nat. Methods 23:868–869.
Nature Biotechnology cover
My cover design on the 7 April 2026 Nature Biotechnology issue shows the dendrogram that represents a cluster of uniquely expressed (or downregulated) genes in human naive stem cells induced from such cells. Within each dendrogram block, the genomic barcode sequence (sampled from Supplementary Table 1) is depicted with a Code 39 barcode. The highlighted barcode is one of those used for cell isolation.
Ishiguro S. et al. A multi-kingdom genetic barcoding system for precise clone isolation (2026) Nature Biotechnology 44:616–629.
Browse my gallery of cover designs.
Happy 2026 π Day—
Art for the 5%
Celebrate π Day (March 14th) and enjoy the art — but only if you're part of the 5%.
Go ahead, see what you can't see.
Ishihara's Tests for Colour Deficiency
Authentic and accurate images of Ishihara's test plates photographed (and lovingly color-corrected) from the 38-plate Ishihara's Tests for Colour Deficiency.
I also provide the position, size, and color of each circle on each test plate.
Symmetric alternatives to the ordinary least squares regression
What immortal hand or eye, could frame thy fearful symmetry? — William Blake, "The Tyger"
This month, we look at symmetric regression, which, unlike simple linear regression, it is reversible — remaining unaltered when the variables are swapped.
Simple linear regression can summarize the linear relationship between two variables `X` and `Y` — for example, when `Y` is considered the response (dependent) and `X` the predictor (independent) variable.
However, there are times when we are not interested (or able) to distinguish between dependent and independent variables — either because they have the same importance or the same role. This is where symmetric regression can help.
Luca Greco, George Luta, Martin Krzywinski & Naomi Altman (2025) Points of significance: Symmetric alternatives to the ordinary least squares regression. Nat. Methods 22:1610–1612.
Beyond Belief Campaign BRCA Art
Fuelled by philanthropy, findings into the workings of BRCA1 and BRCA2 genes have led to groundbreaking research and lifesaving innovations to care for families facing cancer.
This set of 100 one-of-a-kind prints explore the structure of these genes. Each artwork is unique — if you put them all together, you get the full sequence of the BRCA1 and BRCA2 proteins.
