Martin Krzywinski / Genome Sciences Center / Martin Krzywinski / Genome Sciences Center / - contact me Martin Krzywinski / Genome Sciences Center / on Twitter Martin Krzywinski / Genome Sciences Center / - Lumondo Photography
Poetry is just the evidence of life. If your life is burning well, poetry is just the ashLeonard Cohenwatch

circles: exciting

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.


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

find your own path

The source code is freely available. Read how you can compute your own π path!

watch video

Watch the video at Numberphile about my art.

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

2013 Pi Day art

Explore Pi Day art for 2013.

Martin Krzywinski @MKrzywinski
Pi Day art for 2013. (explore)

buy artwork

All the artwork can be purchased from Fine Art America.

Buy 2014 Pi Day Path posters

Buy 2014 Pi Day Circle posters

Buy 2013 Pi Day posters

Buy Love in Pi posters

The art of Pi (π), Phi (φ) and e

the art

Numbers are a lot of fun. They can start conversations—the interesting number paradox is a party favourite. Of course, in the wrong company they can just as easily end conversations.

The art here represents my attempt at transforming famous numbers in mathematics into pretty visual forms. This work is 99% art and 1% data visualization. Because the digits in the numbers are essentially random (as far as we know), the essence of the art is based on randomness.

In a few cases, the art reveals an interesting and unexpected observation. For example, the sequence 999999 in π at digit 762 appears significantly earlier than expected by chance. Or that if you calculate π to 13,099,586 digits you will find love, as encoded by 1114214 in the scheme a=0, b=1, c=2...

Keep in mind that because the digits are random and never terminating, they have the property that they contain all observations about numbers within them. In fact, because the digits go on forever, you'll eventually find π within π.

the numbers

Of these three transcendental numbers, π is the most well known. It is the ratio of a circle's circumference to its diameter (d = πr).

The Golden Ratio (φ) is the attractive proportion of values a and b (a > b) that satisfy (a+b)/a = a/b, which solves to a/b = (1+√5)/2.

Martin Krzywinski @MKrzywinski
The numbers π, φ and e nearly form a right-angled triangle.

The last of the three numbers, e is Euler's number and also known as the base of the natural logarithm. It, too, can be defined geometrically—it is the unique real number, e, for which the function f(x)=ex has a tangent of slope 1 at x=0. Like π, e appears throughout mathematics. For example, e is central in the expression for the normal distribution as well as the definition of entropy. And if you've ever heard of someone talking about log plots ... well, there's e again!

= 3.141592653589793238462643...
= 1.618033988749894848204586...
= 2.718281828459045235360287...

did you see something special?

These three numbers have the curious property that they are almost Pythagorean. In other words, if they are made into sides of a triangle, the triangle is nearly a right-angled triangle (89.1°).

Did you notice how in the 12th decimal point all three numbers have the same digit—9? This accidental similarity generates its own number—the Accidental Similarity Number (ASN).


perl, SVG, Illustrator

Happy Pi Day!

Hug π on March 14th and celebrate Pi Day. Those who favour τ will have to postpone celebrations until July 26th (τ = 2 π). If you're not into details, you may opt to party on July 22nd, which is π approximation day (π ≈ 22/7).

Martin Krzywinski @MKrzywinski buy artwork
2013 Pi Day posters. Celebrate with this post-modern poster. (BUY ARTWORK)
Martin Krzywinski @MKrzywinski buy artwork
2014 Pi Day posters. Celebrate with this modern poster. Pi is folded on a self-avoiding path to maximize the number of neighbouring prime digits. (BUY ARTWORK)

The 2013 posters were inspired by the beautiful AIDS posters by Elena Miska.

Martin Krzywinski @MKrzywinski buy artwork
The 4ness of π. Shown here are the first 2,000 4’s in pi. Each digit is formatted based on its 4-ness, which is a measure of how similar its neighbours are to 4. (...more, BUY ARTWORK)

4ness of Pi (π)

A concept created for this visualization, the iness of a number measures how close each of its digits is to a given number, i.

The iness is calculated for each digit from the average of the relative difference between i and the digit's neighbours.

The 4ness of Pi (π) is a specific case of an iness, for i=4.

Thanks to Lance Bailey for suggesting how to measure iness.


In the sequence of Pi (π) 3.1415 the neighbours of the 4 are 3, 1, 1 and 5. The relative distances to 4 are -1, -3, -1 and 1. The average, which is the 4ness, of this digit (which is also a 4, coincidentally) is -1.5. The 4ness of each of the other digits is computed identically.

In the iness posters, the 4ness is mapped onto a color and the standard deviation of the differences onto a size.

Martin Krzywinski @MKrzywinski buy artwork
The accidental similarity number for π, φ and e created from the first 1,000,000 digits of each number. (...more, BUY ARTWORK)

accidental similarity number

The accidental similarity number is a kind of overlap between numbers. I came up with this concept after creating typographical art about the 4ness of Pi (π).


To construct this number for Pi (π), Phi (φ) and e we first write the numbers on top of each other and then identify positions for which the numbers have the same digit.

3.141 … 3589793 … 7067982 … 7019385 … 
1.618 … 8749894 … 1137484 … 5959395 … 
2.718 … 8459045 … 6427427 … 6279434 … 

These digits are then used to create the accidental similarity number. In thise case,

asn(π,φ,e) = 0.979 …

Martin Krzywinski @MKrzywinski buy artwork
Circos art depicting π, φ and e. (...more, BUY ARTWORK)

Circos numerical art

Numerology is bogus, but art based on numbers is pretty, in a random non-metaphysical way.

These depictions were generated using my Circos software by Cristian Ilies Vasile and myself.

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
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
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
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
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
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
Circos at the British Library Beautiful Science exhibit. (about exhibit)
Martin Krzywinski @MKrzywinski
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
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
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
The Art and Science of Data Visualization (PDF)