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pi day: fun

In Silico Flurries: Computing a world of snow. Scientific American. 23 December 2017

visualization + design

Martin Krzywinski @MKrzywinski
The 2018 Pi Day art celebrates the 30th anniversary of `\pi` day and connects friends stitching road maps from around the world. Pack a sandwich and let's go!

`\pi` Day 2014 Art Posters

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
2018 `\pi` day shrinks the world and celebrates road trips by stitching streets from around the world together. In this version, we look at the boonies, burbs and boutique of `\pi` by drawing progressively denser patches of streets. Let's go places.

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
2017 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
2016 `\pi` approximation day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
2016 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
2015 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
2014 `\pi` approx day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
2014 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
2013 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski
Circular `\pi` art

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.

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.

Martin Krzywinski @MKrzywinski
All art posters are available for purchase.
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 


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


         |     |           
         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   
                  |  |     

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

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 

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

   |     |  
   h  h--p
   |  |     
   H  h   
   H  h   
   |  |     
p--h  h   
|     |     

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

Molecular Case Studies Cover

Fri 06-07-2018

The theme of the April issue of Molecular Case Studies is precision oncogenomics. We have three papers in the issue based on work done in our Personalized Oncogenomics Program (POG).

The covers of Molecular Case Studies typically show microscopy images, with some shown in a more abstract fashion. There's also the occasional Circos plot.

I've previously taken a more fine-art approach to cover design, such for those of Nature, Genome Research and Trends in Genetics. I've used microscopy images to create a cover for PNAS—the one that made biology look like astrophysics—and thought that this is kind of material I'd start with for the MCS cover.

Martin Krzywinski @MKrzywinski
Cover design for Apr 2018 issue of Molecular Case Studies. (details)

Happy 2018 `\tau` Day—Art for everyone

Wed 27-06-2018
Martin Krzywinski @MKrzywinski
You know what day it is. (details)

Universe Superclusters and Voids

Mon 25-06-2018

A map of the nearby superclusters and voids in the Unvierse.

By "nearby" I mean within 6,000 million light-years.

Martin Krzywinski @MKrzywinski
The Universe — Superclustesr and Voids. The two supergalactic hemispheres showing Abell clusters, superclusters and voids within a distance of 6,000 million light-years from the Milky Way. (details)

Datavis for your feet—the 178.75 lb socks

Sat 23-06-2018

In the past, I've been tangentially involved in fashion design. I've also been more directly involved in fashion photography.

It was now time to design my first ... pair of socks.

Martin Krzywinski @MKrzywinski
Some datavis for your feet: the 178.75 lb socks. (get some)

In collaboration with Flux Socks, the design features the colors and relative thicknesses of Rogue olympic weightlifting plates. The first four plates in the stack are the 55, 45, 35, and 25 competition plates. The top 4 plates are the 10, 5, 2.5 and 1.25 lb change plates.

The perceived weight of each sock is 178.75 lb and 357.5 lb for the pair.

The actual weight is much less.

Genes Behind Psychiatric Disorders

Sun 24-06-2018

Find patterns behind gene expression and disease.

Expression, correlation and network module membership of 11,000+ genes and 5 psychiatric disorders in about 6" x 7" on a single page.

Design tip: Stay calm.

Martin Krzywinski @MKrzywinski
Martin Krzywinski @MKrzywinski
An analysis of dust reveals how the presence of men, women, dogs and cats affects the variety of bacteria in a household. Appears on Graphic Science page in December 2015 issue of Scientific American.

More of my American Scientific Graphic Science designs

Gandal M.J. et al. Shared Molecular Neuropathology Across Major Psychiatric Disorders Parallels Polygenic Overlap Science 359 693–697 (2018)

Curse(s) of dimensionality

Tue 05-06-2018
There is such a thing as too much of a good thing.

We discuss the many ways in which analysis can be confounded when data has a large number of dimensions (variables). Collectively, these are called the "curses of dimensionality".

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Curse(s) of dimensionality. (read)

Some of these are unintuitive, such as the fact that the volume of the hypersphere increases and then shrinks beyond about 7 dimensions, while the volume of the hypercube always increases. This means that high-dimensional space is "mostly corners" and the distance between points increases greatly with dimension. This has consequences on correlation and classification.

Altman, N. & Krzywinski, M. (2018) Points of significance: Curse(s) of dimensionality Nature Methods 15:399–400.