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`\pi` Day 2014 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.
For the 2014 `\pi` day, two styles of posters are available: folded paths and frequency circles.
The folded paths show `\pi` on a path that maximizes adjacent prime digits and were created using a protein-folding algorithm.
The frequency circles colourfully depict the ratio of digits in groupings of 3 or 6. Oh, look, there's the Feynman Point!
compute your own path
get simulation code
Download the HP lattice simulation binary. You'll need one of the three 2D methods — I used rem2dm, which does local and pull moves. If you'd like to learn more about the algorithm, read the publication.
A replica exchange Monte Carlo algorithm for protein folding in the HP model. Chris Thachuk, Alena Shmygelska and Holger H Hoos, BMC Bioinformatics 2007, 8:342 (17 Sep 2007).
download batch file
Download the batch file for 64- or 768-digit folding.
run simulation
When you run the 64-digit simulation, you're likely to find a path with E=-23, which is the lowest energy I've been able to sample. On my Intel Xeon E5540 (2.53 GHz) it takes anywhere from 1-30 seconds to find a E=-23 path (there are many possible paths at this energy), depending on the random seed. Here's the output of a typical run of the 64-digit folding simulation
> rem2dm -seq=hppphphphhhpphphhhppphpphhphhhphphppppphppphpphhhpphphpphpppphph
-maxT=220 -numLocalSteps=500 -eng=100 -maxRunTime=60 -traceFile=pi.64
-minT=160 -expID=pi.64 -numReps=10
REMC-HP2D-M
Begin Simulation
0.01: Current Best Solution: -8
0.01: Current Best Solution: -10
0.01: Current Best Solution: -13
0.02: Current Best Solution: -15
0.03: Current Best Solution: -16
0.03: Current Best Solution: -17
0.04: Current Best Solution: -18
0.04: Current Best Solution: -19
0.16: Current Best Solution: -20
0.27: Current Best Solution: -21
0.69: Current Best Solution: -22
36.23: Current Best Solution: -23
Real time: 120
ggslrrsrllssrrlrrllsrrlrrlslslrrsrlssrrsllrslrrlrsllsrsrrlsrssrs
p--h--p
| |
h--h h--p--p--p
| |
p--p h H h--p--p
| | | | |
p--h h--h--p p p--p
| | |
p--p--h h--p p--p p
| | | | |
h--h h h--p--h h--p
| | |
p--h h h--p--H h--p
| | | |
p--p p p--h--h
| |
p p--h--p
| |
p--p--h h
| |
p--p
End Simulation
If you want to apply this to different number (e.g.
φ
or
e
), you'll need to replace the digits with either p or h. Remember, the simulation will try to group the h's together. You can download 1,000,000 of
π
,
φ
and
e
.
The best path I could find for 768 digits is one with E=-223. In 1000s of simulations this solution came up only once. I also saw one path at E=-222. After that, there were many solutions at each of the less optimal energy levels.
If you manage to find a better one, let me know right away!
common problems
segmental fault
If you obtain a segmentation fault,
> ./rem2dlm REMC-HP2D-LM Begin Simulation Real time: 0 Segmentation fault
don't panic just yet. The folding binaries don't do a lot of error checking, so you have to get the input parameters correct.
For example, if you do not include the -eng parameter, the code will segfault.
Try one of the batch files above (64 digit batch file, 768 digit batch file) or the following simple job
> bin/rem2dm -seq=hhpppphhhhpppphh -maxRunTime=5 -eng 10
REMC-HP2D-M
Begin Simulation
3.13877e-17: Current Best Solution: -2
5.49284e-17: Current Best Solution: -3
1.0201e-16: Current Best Solution: -4
1.33398e-16: Current Best Solution: -5
Real time: 5
ggrllslsssrllsls
p--p--p
| |
h h--p
| |
H h
|
H h
| |
p--h h
| |
p--p--p
If this segfaults, then you'll need to recompile the code (see below).
compile code (optional—only if binaries don't work)
Precompiled binaries are available for download directly: rem2dm, rem2dlm, rem2dpm, rem3dm, rem3dlm, rem3dpm.
If these don't work on your system, you need to recompile them. Download the the protein folding code and see INSTALL.txt for compilation instructions.
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.
