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 Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Pi Art Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Hilbertonians - Creatures on the Hilbert Curve
Lips that taste of tears, they say, are the best for kissing.Dorothy Parkerget crankymore quotes

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 2016 Art Posters


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2019 `\pi` has hundreds of digits, hundreds of languages and a special kids' edition.

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2018 `\pi` day

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2017 `\pi` day

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

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

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

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` approx day

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 `\pi` day

Pi Day 2016 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.

This year's `\pi` day art collection celebrates not only the digit but also one of the fundamental forces in nature: gravity.

In February of 2016, for the first time, gravitational waves were detected at the Laser Interferometer Gravitational-Wave Observatory (LIGO).

The signal in the detector was sonified—a process by which any data can be encoded into sound to provide hints at patterns and structure that we might otherwise miss—and we finally heard what two black holes sound like. A buzz and chirp.

The art is featured in the Gravity of Pi article on the Scientific American SA Visual blog.

this year's theme music

All the art was processed while listening to Roses by Coeur de Pirate, a brilliant female French-Canadian songwriter, who sounds like a mix of Patricia Kaas and Lhasa. The lyrics Oublie-moi (Forget me) are fitting with this year's theme of gravity.

Mais laisse-moi tomber, laisse-nous tomber
Laisse la nuit trembler en moi
Laisse-moi tomber, laisse nous tomber
Cette fois

But let me fall, let us fall
Let the night tremble in me
Let me fall, let us fall
This time

The art is generated by running a simulation of gravity in which digits of `\pi` are each assigned a mass and allowed to collide eand orbit each other.

The mathematical details of the simulation can be found in the code section.

exploring force of gravity in `\pi`

A simulation starts with taking `n` digits of `\pi` and arranging them uniformly around a circle. The mass of each digit, `d_i` (e.g. 3), is given by `(1+d)^k` where `k` is a mass power parameter between 0.01 and 1. For example, if `k=0.42` then the mass of 3 is `(1+3)^{0.42} = 1.79`.

collapsing three digits—3.14 collide

The figure below shows the evolution of a simulation with `n=3` digits and `k=1`. The digits 3 and 4 collide to form the digit `3+4 = 7` and immediately collides with 1 to form `7+1=8`. With only one mass left in the system, the simulation stops.


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The evolution of a simulation of gravity using `n=3` digits of `\pi` and the mass power `k=1`. The masses are initialized with zero velocity. (zoom)

adding initial velocity to each mass

When masses have initial velocities, the patterns quickly start to get interesting. In the figure above, the masses are initalized with zero velocity. As soon as the simulation, each mass immediately starts to move directly towards the center of mass of the other two masses.

When the initial velocity is non-zero, such as in the figure below, the masses don't immediately collapse towards one another. The masses first travel with their initial velocity but immediately the gravitational force imparts acceleration that alters this velocity. In the examples below, only those simulations in which the masses collapsed within a time cutoff are shown.


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The evolution of a simulation of gravity using `n=3` digits of `\pi` and the mass power `k=1` in which all masses collapsed. The masses are initialized with a random velocity. (zoom)

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The evolution of 16 simulations of gravity using `n=3` digits of `\pi` and the mass power `k=1` in which all masses collapsed. The masses are initialized with a random velocity. (zoom)

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The evolution of 49 simulations of gravity using `n=3` digits of `\pi` and the mass power `k=1` in which all masses collapsed. The masses are initialized with a random velocity. (zoom)

allowing the simulation to evolve

Depending on the initial velocities, some systems collapse very quickly, which doesn't make for interesting patterns.

For example, the simulations above evolved over 100,000 steps and in some cases the masses collapsed within 10,000 steps. In the figure below, I require that the system evolves for at least 15,000 steps before collapsing. Lovely doddles, don't you think?


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The evolution of 36 simulations of gravity using `n=3` digits of `\pi` and the mass power `k=1` in which all masses collapsed after a minimum amount of time. The masses are initialized with a random velocity. (zoom)

exploring ensembles

When a simulation is repeated with different initial conditions, the set of outcomes is called an ensemble.

Below, I repeat the simulation 100 times with `n=3` and `k=0.2`, each time with slightly different initial velocity. The velocities have their `x`- and `y`-components normally distributed with zero mean and a fixed variance. Each of the four ensembles has its simulations evolve over progressively more time steps: 5,000, 7,500, 10,000, and 20,000.

You can see that with 5,000 steps the masses don't yet have a chance to collide. After 7,500, there have been collisions in a small number of systems. The blue mass corresponds to the 3 colliding with 4 and the green mass to 1 colliding with 4. After 10,000, even more collisions are seen and in 3 cases we see total collapse (all three digits collided). After 20,000,


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The evolution of 100 simulations of gravity over total time `t` using `n=3` digits of `\pi` and the mass power `k=0.2`. Within each ensemble, the masses are initialized with a different random velocity in each instance. (zoom)

varying masses

The value of `k` greatly impacts the outcome of the simulation. When `k` is very small, all the digits have essentially the same mass. For example, when `k=0.01` the 0 has a mass of 1 and 9 has a mass of 1.02.

When `k` is large, the difference in masses is much greater. For example, for `k=2` the lightest mass is `(1+0)^2=1` and the heaviest `(1+9)^2=10`. Because the acceleration of a mass is proportional to the mass that is attracting it, in a pair of masses the light mass will accelerate faster.


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Larger values of `k` create greater diversity among the masses. Shown are simulations of 36 digits with `k` values varying from 0.1 to 3. The total mass of the system, `\Sigma m`, is also shown.`. (zoom)

increasing number of masses

As the number of digits is increased, the pattern of collapse doesn't qualitatively change.


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Simulations for `n = 50, 100, 250` and `500` masses with `k = 0.5`. (zoom)

gravity makes beautiful doodles

I ran a large number of simulations. For various values of `n` and `k`, I repeated the simulation several times to sample different intial velocities.


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Thumbnails of `\pi` digit orbital simulations for various values of `n` and `k`. (zoom)

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Gravitational attraction paths of the first 100 digits of `\pi` for `k = 0.3`, `0.6` and `0.8` with initial velocities randomly set. Three instances of the simulation are shown, each with different intital velocities. (zoom)

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Gravitational attraction paths of the first 60 digits of `\pi` for `k = 1`. After 100,000 time steps, some masses are still orbiting within the canvas (e.g. green mass at bottom right). The numbers next to the masses correspond to the digits (those around the circle are the first 50 digits of `\pi` and others are the sum (mod 10) of digits that collided). Also shown next to the numbers is their mass, index and indices of masses that formed them. (zoom)

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Gravitational attraction paths of the first 50 digits of `\pi` for `k = 0.4`. The numbers next to the masses correspond to the digits (those around the circle are the first 50 digits of `\pi` and others are the sum (mod 10) of digits that collided). (zoom)

Below is a great example of how a stable orbital pattern of a pair of masses can be disrupted by the presence of another mass. You can see on the left that once the light red mass moves away from the orange/green pair, they settle into a stable pattern.


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Gravitational attraction paths of the first 50 digits of `\pi` for `k = 0.9`. The numbers next to the masses correspond to the digits (those around the circle are the first 50 digits of `\pi` and others are the sum (mod 10) of digits that collided). (zoom)

The figure below shows one of my favourite patterns. As the digits collide, three masses remain, which leave the system. They remain under each other's gravitational influence, but are moving too quickly to return to the canvas within the time of the simulation.


Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Gravitational attraction paths of the first 90 digits of `\pi` for `k = 0.8`. The digits collide, leaving three rapidly-moving masses, which leave the canvas. (zoom)

how the idea developed

interactive gravity simulator

Use this fun inteactive gravity simulator if you want to drop your own masses and watch them orbit.

VIEW ALL

news + thoughts

Analyzing outliers: Robust methods to the rescue

Sat 30-03-2019
Robust regression generates more reliable estimates by detecting and downweighting outliers.

Outliers can degrade the fit of linear regression models when the estimation is performed using the ordinary least squares. The impact of outliers can be mitigated with methods that provide robust inference and greater reliability in the presence of anomalous values.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Analyzing outliers: Robust methods to the rescue. (read)

We discuss MM-estimation and show how it can be used to keep your fitting sane and reliable.

Greco, L., Luta, G., Krzywinski, M. & Altman, N. (2019) Points of significance: Analyzing outliers: Robust methods to the rescue. Nature Methods 16:275–276.

Background reading

Altman, N. & Krzywinski, M. (2016) Points of significance: Analyzing outliers: Influential or nuisance. Nature Methods 13:281–282.

Two-level factorial experiments

Fri 22-03-2019
To find which experimental factors have an effect, simultaneously examine the difference between the high and low levels of each.

Two-level factorial experiments, in which all combinations of multiple factor levels are used, efficiently estimate factor effects and detect interactions—desirable statistical qualities that can provide deep insight into a system.

They offer two benefits over the widely used one-factor-at-a-time (OFAT) experiments: efficiency and ability to detect interactions.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Two-level factorial experiments. (read)

Since the number of factor combinations can quickly increase, one approach is to model only some of the factorial effects using empirically-validated assumptions of effect sparsity and effect hierarchy. Effect sparsity tells us that in factorial experiments most of the factorial terms are likely to be unimportant. Effect hierarchy tells us that low-order terms (e.g. main effects) tend to be larger than higher-order terms (e.g. two-factor or three-factor interactions).

Smucker, B., Krzywinski, M. & Altman, N. (2019) Points of significance: Two-level factorial experiments Nature Methods 16:211–212.

Background reading

Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments.. Nature Methods 11:597–598.

Happy 2019 `\pi` Day—
Digits, internationally

Tue 12-03-2019

Celebrate `\pi` Day (March 14th) and set out on an exploration explore accents unknown (to you)!

This year is purely typographical, with something for everyone. Hundreds of digits and hundreds of languages.

A special kids' edition merges math with color and fat fonts.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
116 digits in 64 languages. (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
223 digits in 102 languages. (details)

Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day, 2017 `\pi` Day and 2018 `\pi` Day.

Tree of Emotional Life

Sun 17-02-2019

One moment you're :) and the next you're :-.

Make sense of it all with my Tree of Emotional life—a hierarchical account of how we feel.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A section of the Tree of Emotional Life.

Find and snap to colors in an image

Sat 29-12-2018

One of my color tools, the colorsnap application snaps colors in an image to a set of reference colors and reports their proportion.

Below is Times Square rendered using the colors of the MTA subway lines.


Colors used by the New York MTA subway lines.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Times Square in New York City.
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Times Square in New York City rendered using colors of the MTA subway lines.
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Granger rainbow snapped to subway lines colors from four cities. (zoom)

Take your medicine ... now

Wed 19-12-2018

Drugs could be more effective if taken when the genetic proteins they target are most active.

Design tip: rediscover CMYK primaries.

More of my American Scientific Graphic Science designs

Ruben et al. A database of tissue-specific rhythmically expressed human genes has potential applications in circadian medicine Science Translational Medicine 10 Issue 458, eaat8806.