Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - contact me Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca on Twitter Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Lumondo Photography
This love loves love. It's a strange love, strange love.Liz Fraserwatch

pi: beautiful


Circos at British Library Beautiful Science exhibit—Feb 20–May 26


visualization + design

Typography geek? If you like the geometry and mathematics of these posters, you may enjoy something more lettered. Visions of type: Type Peep Show: The Private Curves of Letters posters.

← art(π,φ,e)

2013 Pi Day Art Posters — March 14

download

numbers.tgz
1,000,000 digits of π, φ, e and ASN.

watch video

Watch the video at Numberphile about my art.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Numberphile video — Pi is Beautiful. (watch)

2014 Pi Day art

Explore Pi Day art for 2014.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Pi Day art for 2014. (explore)

buy artwork

All the artwork can be purchased from Fine Art America.

buy Pi day posters

buy Love in Pi posters

transcend, don't repeat, yourself

Proclus got it right when he said (as quoted by M. Kline in Mathematical Thought from Ancient to Modern Times)

Wherever there is number, there is beauty.

So let's explore what Pi looks like with something whimsical and pretty and colourful. Rational art of the highly irrational, a regime where beauty runs with her hair down and lets her "ribbons to flow confusedly." Robert Herrick says it well in Sweet Disorder,

I see a wild civility;—
Do more bewitch me, than when art
Is too precise in every part.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Each digit is represented by a dot of a different color. The inner grey dots appear to glimmer—this is the luminance effect in action.

The posters explore the relationship between adjacent digits in Pi, which are encoded by color using the scheme shown above. The design appears to shimmer due to the luminance effect. In some versions of the poster, adjacent identical (or similar) digits are connected by lines.

Want more math + art? Discover the Accidental Similarity Number and other number art. Find humor in my poster of the first 2,000 4s of Pi.

The recipe for each poster is included and gives the color of the ith outer/inner circle. π[i] is used to represent the ith digit of π. For example, the recipe

π[i] / π[i+1]

generates a poster whose outer circle color encodes the ith digit and the inner circle color encodes the next digit (i+1). In this scheme, inner and outer circles of adjacent positions have the same color.

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

source and methods

The posters were generated automatically with a Perl script that generated SVG files. Post processing and layout was done in Illustrator. If you are interested in depicting your favourite number this way, let me know.

The design was inspired by the beautiful AIDS posters by Elena Miska.

love in Pi—you can find it here

I calculated Pi to 13,099,586 digits and then I found love.

It's fun to look for words in Pi. I wanted to know the first time that love appears in Pi. When encoded using the scheme a=0, b=1, ..., z=25, love is the digit 1114214. This digit appears first at position 13,099,586 (...892199163111142148187311392...). And, of course, infinitely many times after that.

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)
Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)
Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

If you use the scheme a=1, b=2, ..., z=26, then love becomes 1215225. This is first seen at 6,317,696 (...610311912912152256606850141...).

Because the digits of Pi never repeat and are distributed randomly (as far as we know), if you look long enough you'll find all the words in Pi infinitely many times.

700 digits (20 x 35)

π[i] / grey, 80% opacity

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1], 80% opacity

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

2,800 (40 x 70) digits

π[i] / grey, 80% opacity (equal neighbours connected)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1], 80% opacity (equal neighbours connected)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

— / π[i+1] (equal neighbours connected, unconnected digits not shown)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1] (equal neighbours connected with line width proportional to difference in neighbour digits d∈{0,1,2}, unconnected digits not shown)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1] (equal neighbours connected with line width proportional to difference in neighbour digits d∈{0..5}, unconnected digits not shown)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

Pi (π): — / red (equal neighbours connected, unconnected digits not shown)
Phi (φ): — / white (equal neighbours connected, unconnected digits not shown)
e: — / grey (equal neighbours connected, unconnected digits not shown)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

11,400 (80 x 140) digits

π[i] / grey, 80% opacity (equal neighbours connected)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1], 80% opacity (equal neighbours connected)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1] &>

π[i] / grey, 80% opacity (equal neighbours connected, unconnected digits not shown)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1], 80% opacity (equal neighbours connected, unconnected digits not shown)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

news + thoughts

Mind your p's and q's

Sat 29-03-2014

In the April Points of Significance Nature Methods column, we continue our and consider what happens when we run a large number of tests.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Comparing Samples — Part II — Multiple Testing. (read)

Observing statistically rare test outcomes is expected if we run enough tests. These are statistically, not biologically, significant. For example, if we run N tests, the smallest P value that we have a 50% chance of observing is 1–exp(–ln2/N). For N = 10k this P value is Pk=10kln2 (e.g. for 104=10,000 tests, P4=6.9×10–5).

We discuss common correction schemes such as Bonferroni, Holm, Benjamini & Hochberg and Storey's q and show how they impact the false positive rate (FPR), false discovery rate (FDR) and power of a batch of tests.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part II — Multiple Testing Nature Methods 11:215-216.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I — t-tests Nature Methods 11:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, P values and t-tests Nature Methods 10:1041-1042.

Happy Pi Day— go to planet π

Fri 21-03-2014

Celebrate Pi Day (March 14th) with the art of folding numbers. This year I take the number up to the Feynman Point and apply a protein folding algorithm to render it as a path.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Digits of Pi form landmass and shoreline. (details)

For those of you who liked the minimalist and colorful digit grid, I've expanded on the concept to show stacked ring plots of frequency distributions.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Frequency distribution of digits of Pi in groups of 6 up to the Feynman Point. (details)

And if spirals are your thing...

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Frequency distribution of digits of Pi in groups of 4 up to digit 4,988. (details)

Have data, will compare

Fri 07-03-2014

In the March Points of Significance Nature Methods column, we continue our discussion of t-tests from November (Significance, P values and t-tests).

We look at what happens how uncertainty of two variables combines and how this impacts the increased uncertainty when two samples are compared and highlight the differences between the two-sample and paired t-tests.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Comparing Samples — Part I. (read)

When performing any statistical test, it's important to understand and satisfy its requirements. The t-test is very robust with respect to some of its assumptions, but not others. We explore which.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I Nature Methods 11:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, P values and t-tests Nature Methods 10:1041-1042.

Circos at British Library Beautiful Science Exhibit

Thu 06-03-2014

Beautiful Science explores how our understanding of ourselves and our planet has evolved alongside our ability to represent, graph and map the mass data of the time. The exhibit runs 20 February — 26 May 2014 and is free to the public. There is a good Nature blog writeup about it, a piece in The Guardian, and a great video that explains the the exhibit narrated by Johanna Kieniewicz, the curator.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Circos at the British Library Beautiful Science exhibit. (about exhibit)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Mailed invitation to the exhibit features my science art. (zoom)

I am privileged to contribute an information graphic to the exhibit in the Tree of Life section. The piece shows how sequence similarity varies across species as a function of evolutionary distance. The installation is a set of 6 30x30 cm backlit panels. They look terrific.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Circos Circles of Life installation at Beautiful Science exhibit at the British Library. (zoom)

Think outside the bar—box plots

Fri 31-01-2014

Quick, name three chart types. Line, bar and scatter come to mind. Perhaps you said pie too—tsk tsk. Nobody ever thinks of the box plot.

Box plots reveal details about data without overloading a figure with a full frequency distribution histogram. They're easy to compare and now easy to make with BoxPlotR (try it). In our fifth Points of Significance column, we take a break from the theory to explain this plot type and—I hope— convince you that they're worth thinking about.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Visualizing samples with box plots. (read)

The February issue of Nature Methods kicks the bar chart two more times: Dan Evanko's Kick the Bar Chart Habit editorial and a Points of View: Bar charts and box plots column by Mark Streit and Nils Gehlenborg.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Visualizing samples with box plots Nature Methods 11:119-120.

Wired Data|Life 2013 talk

Thu 05-12-2013

I recently presented at the Wired Data|Life 2013 conference, sharing my thoughts on The Art and Science of Data Visualization.

For specialists, visualizations should expose detail to allow for exploration and inspiration. For enthusiasts, they should provide context, integrate facts and inform. For the layperson, they should capture the essence of the topic, narrate a story and deligt.

Wired's Brandon Keim wrote up a short article about me and some of my work—Circle of Life: The Beautiful New Way to Visualize Biological Data.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The Art and Science of Data Visualization (PDF)