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π Day 2024 Art Posters - A community garden of digits of π
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
2024 π DAY | 768 digits of `\pi` as a garden at night. Explore the gardens (BUY ARTWORK)

`\pi` Day 2014 Art Posters


Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2021 π DAY | Good things grow for those who wait.' edition.

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2019 π DAY | Hundreds of digits, hundreds of languages and a special kids' edition.

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2018 π DAY | Street maps to new destinations.

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2017 π DAY | Imagine the sky in a new way.


Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 π APPROXIMATION DAY | What would happen if about right was right.

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 π DAY | These digits really fall for each other.

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 π DAY | A transcendental experience.

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 π APPROXIMATION DAY | Spirals into roughness.


Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 π DAY | Hypnotizes you into looking.

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 π DAY | Come into the fold.

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 π DAY | Where it started.

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
CIRCULAR π 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.

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.

news + thoughts

Propensity score matching

Mon 16-09-2024

I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player

In many experimental designs, we need to keep in mind the possibility of confounding variables, which may give rise to bias in the estimate of the treatment effect.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Propensity score matching. (read)

If the control and experimental groups aren't matched (or, roughly, similar enough), this bias can arise.

Sometimes this can be dealt with by randomizing, which on average can balance this effect out. When randomization is not possible, propensity score matching is an excellent strategy to match control and experimental groups.

Kurz, C.F., Krzywinski, M. & Altman, N. (2024) Points of significance: Propensity score matching. Nat. Methods 21:1770–1772.

Nasa to send our human genome discs to the Moon

Sat 23-03-2024

We'd like to say a ‘cosmic hello’: mathematics, culture, palaeontology, art and science, and ... human genomes.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
SANCTUARY PROJECT | A cosmic hello of art, science, and genomes. (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
SANCTUARY PROJECT | Benoit Faiveley, founder of the Sanctuary project gives the Sanctuary disc a visual check at CEA LeQ Grenoble (image: Vincent Thomas). (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
SANCTUARY PROJECT | Sanctuary team examines the Life disc at INRIA Paris Saclay (image: Benedict Redgrove) (details)

Comparing classifier performance with baselines

Fri 22-03-2024

All animals are equal, but some animals are more equal than others. —George Orwell

This month, we will illustrate the importance of establishing a baseline performance level.

Baselines are typically generated independently for each dataset using very simple models. Their role is to set the minimum level of acceptable performance and help with comparing relative improvements in performance of other models.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Comparing classifier performance with baselines. (read)

Unfortunately, baselines are often overlooked and, in the presence of a class imbalance, must be established with care.

Megahed, F.M, Chen, Y-J., Jones-Farmer, A., Rigdon, S.E., Krzywinski, M. & Altman, N. (2024) Points of significance: Comparing classifier performance with baselines. Nat. Methods 21:546–548.

Happy 2024 π Day—
sunflowers ho!

Sat 09-03-2024

Celebrate π Day (March 14th) and dig into the digit garden. Let's grow something.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2024 π DAY | A garden of 1,000 digits of π. (details)

How Analyzing Cosmic Nothing Might Explain Everything

Thu 18-01-2024

Huge empty areas of the universe called voids could help solve the greatest mysteries in the cosmos.

My graphic accompanying How Analyzing Cosmic Nothing Might Explain Everything in the January 2024 issue of Scientific American depicts the entire Universe in a two-page spread — full of nothing.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
How Analyzing Cosmic Nothing Might Explain Everything. Text by Michael Lemonick (editor), art direction by Jen Christiansen (Senior Graphics Editor), source: SDSS

The graphic uses the latest data from SDSS 12 and is an update to my Superclusters and Voids poster.

Michael Lemonick (editor) explains on the graphic:

“Regions of relatively empty space called cosmic voids are everywhere in the universe, and scientists believe studying their size, shape and spread across the cosmos could help them understand dark matter, dark energy and other big mysteries.

To use voids in this way, astronomers must map these regions in detail—a project that is just beginning.

Shown here are voids discovered by the Sloan Digital Sky Survey (SDSS), along with a selection of 16 previously named voids. Scientists expect voids to be evenly distributed throughout space—the lack of voids in some regions on the globe simply reflects SDSS’s sky coverage.”

voids

Sofia Contarini, Alice Pisani, Nico Hamaus, Federico Marulli Lauro Moscardini & Marco Baldi (2023) Cosmological Constraints from the BOSS DR12 Void Size Function Astrophysical Journal 953:46.

Nico Hamaus, Alice Pisani, Jin-Ah Choi, Guilhem Lavaux, Benjamin D. Wandelt & Jochen Weller (2020) Journal of Cosmology and Astroparticle Physics 2020:023.

Sloan Digital Sky Survey Data Release 12

constellation figures

Alan MacRobert (Sky & Telescope), Paulina Rowicka/Martin Krzywinski (revisions & Microscopium)

stars

Hoffleit & Warren Jr. (1991) The Bright Star Catalog, 5th Revised Edition (Preliminary Version).

cosmology

H0 = 67.4 km/(Mpc·s), Ωm = 0.315, Ωv = 0.685. Planck collaboration Planck 2018 results. VI. Cosmological parameters (2018).

Error in predictor variables

Tue 02-01-2024

It is the mark of an educated mind to rest satisfied with the degree of precision that the nature of the subject admits and not to seek exactness where only an approximation is possible. —Aristotle

In regression, the predictors are (typically) assumed to have known values that are measured without error.

Practically, however, predictors are often measured with error. This has a profound (but predictable) effect on the estimates of relationships among variables – the so-called “error in variables” problem.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Error in predictor variables. (read)

Error in measuring the predictors is often ignored. In this column, we discuss when ignoring this error is harmless and when it can lead to large bias that can leads us to miss important effects.

Altman, N. & Krzywinski, M. (2024) Points of significance: Error in predictor variables. Nat. Methods 21:4–6.

Background reading

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nat. Methods 12:999–1000.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nat. Methods 13:541–542 (2016).

Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nat. Methods 16:451–452.

Martin Krzywinski | contact | Canada's Michael Smith Genome Sciences CentreBC Cancer Research CenterBC CancerPHSA
Google whack “vicissitudinal corporealization”
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