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pi day: fun


DNA on 10th — street art, wayfinding and font


visualization + design

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The 2019 Pi Day art celebrates digits of `\pi` with hundreds of languages and alphabets. If you're a kid at heart—rejoice—there's a special edition for you!

`\pi` Day 2015 Art Posters


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2019 `\pi` has hundreds of digits, hundreds of languages and a special kids' edition.

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2018 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2017 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` approximation day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` approx day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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. 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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
All art posters are available for purchase.
I take custom requests.

Not a circle in sight in the 2015 `\pi` day art. Try to figure out how up to 612,330 digits are encoded before reading about the method. `\pi`'s transcendental friends `\phi` and `e` are there too—golden and natural. Get it?

This year's `\pi` day is particularly special. The digits of time specify a precise time if the date is encoded in North American day-month-year convention: 3-14-15 9:26:53.

The art has been featured in Ana Swanson's Wonkblog article at the Washington Post—10 Stunning Images Show The Beauty Hidden in `\pi`.

This year's art has a modern Bauhaus style. Sharp edges, lines and solid colors. Potato farms from space. CPUs from up close. If the pieces look like the art of Piet Mondrian, you'd be right.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
3,628 digits of `\pi` in a 6 level treemap. Uniform line thickness. Bauhaus prime colors. (posters, BUY ARTWORK)

The digits of `pi` are encoded in something that looks like a treemap. I explain how this is done in the methods section, but before reading it, try to see if you can figure out how it's done.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
2,258 digits of `\phi`, 3,855 digits of `e` and 3,628 digits of `\pi` in 6 level treemaps. Uniform line thickness. Brewer palette sequential greys. (posters, BUY ARTWORK)

I briefly experimented with the 4-color theorem in trying to apply color to the treemap, but it turned out to lack interesting stucture. Well, at least some graphs were made.

I experimented with different treemap resolutions. For treemaps that use an outline around each rectangle, I decided to stop at 8 levels, at which 111,469 digits of `pi` can be encoded.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
3,628 digits of `\pi` in a 6 level treemap. Uniform line thickness. Bauhaus prime colors. (posters, BUY ARTWORK)

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
20,244 digits of `\pi` in a 7 level treemap. Uniform line thickness. Bauhaus prime colors. (posters, BUY ARTWORK)

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
111,469 digits of `\pi` in an 8 level treemap. Uniform line thickness, slightly thinner than for the 7-level map. Bauhaus prime colors. (posters, BUY ARTWORK)

I also made a level 9 treemap without the outlines, which encoded 612,330 digits. When rendered at 20,833 × 20,833 pixels (I needed the image in bitmap form to provide the posters for sale), some regions are essentially a pixel in size, as seen in the 1-1 crop below.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
612,330 digits of `\pi` in an 9 level treemap. Bauhaus prime colors. (posters, BUY ARTWORK)

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
1-1 crop of 612,330 digits of `\pi` in an 9 level treemap. Bauhaus prime colors. (posters)

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news + thoughts

Scientific data visualization: Aesthetic for diagrammatic clarity

Mon 13-01-2020

The scientific process works because all its output is empirically constrained.

My chapter from The Aesthetics of Scientific Data Representation, More than Pretty Pictures, in which I discuss the principles of data visualization and connect them to the concept of "quality" introduced by Robert Pirsig in Zen and the Art of Motorcycle Maintenance.

Yearning for the Infinite — Aleph 2

Mon 18-11-2019

Discover Cantor's transfinite numbers through my music video for the Aleph 2 track of Max Cooper's Yearning for the Infinite (album page, event page).

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Yearning for the Infinite, Max Cooper at the Barbican Hall, London. Track Aleph 2. Video by Martin Krzywinski. Photo by Michal Augustini. (more)

I discuss the math behind the video and the system I built to create the video.

Hidden Markov Models

Mon 18-11-2019

Everything we see hides another thing, we always want to see what is hidden by what we see.
—Rene Magritte

A Hidden Markov Model extends a Markov chain to have hidden states. Hidden states are used to model aspects of the system that cannot be directly observed and themselves form a Markov chain and each state may emit one or more observed values.

Hidden states in HMMs do not have to have meaning—they can be used to account for measurement errors, compress multi-modal observational data, or to detect unobservable events.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Hidden Markov Models. (read)

In this column, we extend the cell growth model from our Markov Chain column to include two hidden states: normal and sedentary.

We show how to calculate forward probabilities that can predict the most likely path through the HMM given an observed sequence.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Hidden Markov Models. Nature Methods 16:795–796.

Background reading

Altman, N. & Krzywinski, M. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.

Hola Mundo Cover

Sat 21-09-2019

My cover design for Hola Mundo by Hannah Fry. Published by Blackie Books.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Hola Mundo by Hannah Fry. Cover design is based on my 2013 `\pi` day art. (read)

Curious how the design was created? Read the full details.

Markov Chains

Tue 30-07-2019

You can look back there to explain things,
but the explanation disappears.
You'll never find it there.
Things are not explained by the past.
They're explained by what happens now.
—Alan Watts

A Markov chain is a probabilistic model that is used to model how a system changes over time as a series of transitions between states. Each transition is assigned a probability that defines the chance of the system changing from one state to another.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Markov Chains. (read)

Together with the states, these transitions probabilities define a stochastic model with the Markov property: transition probabilities only depend on the current state—the future is independent of the past if the present is known.

Once the transition probabilities are defined in matrix form, it is easy to predict the distribution of future states of the system. We cover concepts of aperiodicity, irreducibility, limiting and stationary distributions and absorption.

This column is the first part of a series and pairs particularly well with Alan Watts and Blond:ish.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.

1-bit zoomable gigapixel maps of Moon, Solar System and Sky

Mon 22-07-2019

Places to go and nobody to see.

Exquisitely detailed maps of places on the Moon, comets and asteroids in the Solar System and stars, deep-sky objects and exoplanets in the northern and southern sky. All maps are zoomable.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
3.6 gigapixel map of the near side of the Moon, annotated with 6,733. (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
100 megapixel and 10 gigapixel map of the Solar System on 20 July 2019, annotated with 758k asteroids, 1.3k comets and all planets and satellites. (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
100 megapixle and 10 gigapixel map of the Northern Celestial Hemisphere, annotated with 44 million stars, 74,000 deep-sky objects and 3,000 exoplanets. (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
100 megapixle and 10 gigapixel map of the Southern Celestial Hemisphere, annotated with 69 million stars, 88,000 deep-sky objects and 1000 exoplanets. (details)