Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / - contact me Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / on Twitter Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / - Lumondo Photography Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / - Pi Art Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / - Hilbertonians - Creatures on the Hilbert CurveMartin Krzywinski / Canada's Michael Smith Genome Sciences Centre / - Pi Day 2020 - Piku
Here we are now at the middle of the fourth large part of this talk.Pepe Deluxeget nowheremore quotes

3.14: fun

Scientific graphical abstracts — design guidelines

visualization + design

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
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81 digits of `\pi` as a forest of trees: standard, bat cave and underwater editions. ( BUY ARTWORK )
Martin Krzywinski @MKrzywinski
The 2021 Pi Day art celebrates the digits of `\pi` with a forest! Visit the bat cave and underwater ecosystems for the full experience.

`\pi` Day 2016 Art Posters

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski
2021 `\pi` reminds us that good things grow for those who wait.' edition.

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

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski
2018 `\pi` day stitches street maps into new destinations.

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski
2017 `\pi` day imagines the sky in a new way.

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski
2016 `\pi` approximation day wonders what would happen if about right was right.

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski
2016 `\pi` day sees digits really fall for each other.

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski
2015 `\pi` day maps transcendentally.

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski
2014 `\pi` approx day spirals into roughness.

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski
2014 `\pi` day hypnotizes you into looking.

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski
2014 `\pi` day

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski
2013 `\pi` day is where it started

Pi Day 2016 Art Posters
 / Martin Krzywinski @MKrzywinski
Circular `\pi` art and other distractions

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
Most of the art is available for purchase as framed prints and, yes, even pillows. Sleep's never been more important — 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

simulating gravity in 2d

The gravitational force between two masses `m_1` located at `(x_1,y_1)` and `m_2` located at `(x_2,y_2)` is given by

$$F = \frac{G m_1 m_2}{r^2} \tag{1} $$

where `r` is the distance between the masses given by

$$r = \sqrt{ \Delta x ^2 + \Delta y ^2 } = \sqrt{ (x_2-x_1)^2 + (y_2-y_1)^2 } \tag{2} $$

The force is directed along the vector formed by `r` and can be decomposed into `x` and `y` components using \begin{align} F_x &= F \frac{ \Delta x}{r} = F \frac{x_2-x_1}{r} \tag{3} \\ F_y &= F \frac{ \Delta y}{r} =F \frac{y_2-y_1}{r} \tag{4} \end{align}

The acceleration of each mass can be obtained using `F = ma` and similarly decomposed into `x` and `y` components \begin{align} a_{1x} &= \frac { F_{1x} }{ m_1} = \frac{G m_2 \Delta x}{r^3} \tag{5} \\ a_{1y} &= \frac { F_{1y} }{ m_1} = \frac{G m_2 \Delta y}{r^3} \tag{6} \\ a_{2x} &= \frac { F_{2x} }{ m_2} = -\frac{G m_1 \Delta x}{r^3} \tag{7} \\ a_{2y} &= \frac { F_{2y} }{ m_2} = -\frac{G m_1 \Delta y}{r^3} \tag{8} \end{align}

When there are `n` masses in the system, the acceleration of mass `i` is the sum of the accelerations due to all other masses \begin{align} a_{ix} &= \sum_{i \ne j} \frac{G m_j \Delta x_{ij}}{r_{ij}^3} \tag{9} \\ a_{iy} &= \sum_{i \ne j} \frac{G m_j \Delta y_{ij}}{r_{ij}^3} \tag{10} \end{align}

The equations of motion for the masses over a period of time `\Delta t` are

\begin{align} \Delta v_x &= \Delta t a_x \tag{11} \\ \Delta v_y &= \Delta t a_y \tag{12} \\ \Delta x &= \Delta t \left( v_x + a_x \frac{\Delta t}{2} \right) \tag{13} \\ \Delta y &= \Delta t \left( v_y + a_y \frac{\Delta t}{2} \right) \tag{14} \end{align}

numerical simulation

There are various ways in which the numerical simulation can be performed. The Euler, Verlet, Runge-Kutta methods are perhaps the most common. I use the Verlet approach.

Using the equations of motions above, the Verlet simulation goes as follows

  1. calculate acceleration, `a_1` (eq 9,10)
  2. update position (eq 13,14)
  3. calculate new acceleration, `a_2` (eq 9,10)
  4. update velocity using `(a_1+a_2)/2` (eq 7,8)

The masses are initially uniformly distributed on a circle and given a zero initial velocity or a normally distributed random velocity.

I ran about 10,000 individual simulations with different values of `n` and `k` and collected ones that stood out as pretty.


The size of a mass is taken to be `s = m^{1/3}`. When two masses, `m_1` and `m_2` come within a distance of `\left( s_1 + s_2 \right)(1-z)` of each other, they collide. Here `z` is a collision margin parameter that I set to either `z=0` or `z=0.25`.

During the collision, a new body is created with mass `M = m_1 + m_2` given a speed that conserves momentum in the collision. \begin{align} v_x &= \frac{m_1 v_{1x} + m_2 v_{2x} }{M} \\ v_y &= \frac{m_1 v_{1y} + m_2 v_{2y} }{M} \end{align}


For my simulation, the following values are used

  • `G = 100`
  • mass for each digit, `d` is `(1+d)^k`
  • masses placed on circle with radius `216`
  • when randomized, `(v_x,v_y) \sim N(0,1)`
  • `\Delta t = 0.01`
  • simulation runs for up to 100,000 steps
  • canvas size is `1440 \times 1440`


news + thoughts

Music for the Moon: Flunk's 'Down Here / Moon Above'

Sat 29-05-2021

The Sanctuary Project is a Lunar vault of science and art. It includes two fully sequenced human genomes, sequenced and assembled by us at Canada's Michael Smith Genome Sciences Centre.

The first disc includes a song composed by Flunk for the (eventual) trip to the Moon.

But how do you send sound to space? I describe the inspiration, process and art behind the work.

Martin Krzywinski @MKrzywinski
The song 'Down Here / Moon Above' from Flunk's new album History of Everything Ever is our song for space. It appears on the Sanctuary genome discs, which aim to send two fully sequenced human genomes to the Moon. (more)

Browse the genome discs.

Happy 2021 `\pi` Day—
A forest of digits

Sun 14-03-2021

Celebrate `\pi` Day (March 14th) and finally see the digits through the forest.

Martin Krzywinski @MKrzywinski
The 26th tree in the digit forest of `\pi`. Why is there a flower on the ground?. (details)

This year is full of botanical whimsy. A Lindenmayer system forest – deterministic but always changing. Feel free to stop and pick the flowers from the ground.

Martin Krzywinski @MKrzywinski
The first 46 digits of `\pi` in 8 trees. There are so many more. (details)

And things can get crazy in the forest.

Martin Krzywinski @MKrzywinski
A forest of the digits of '\pi`, by ecosystem. (details)

Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day, 2017 `\pi` Day, 2018 `\pi` Day and 2019 `\pi` Day.

Testing for rare conditions

Sun 30-05-2021

All that glitters is not gold. —W. Shakespeare

The sensitivity and specificity of a test do not necessarily correspond to its error rate. This becomes critically important when testing for a rare condition — a test with 99% sensitivity and specificity has an even chance of being wrong when the condition prevalence is 1%.

We discuss the positive predictive value (PPV) and how practices such as screen can increase it.

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Testing for rare conditions. (read)

Altman, N. & Krzywinski, M. (2021) Points of significance: Testing for rare conditions. Nature Methods 18:224–225.

Standardization fallacy

Tue 09-02-2021

We demand rigidly defined areas of doubt and uncertainty! —D. Adams

A popular notion about experiments is that it's good to keep variability in subjects low to limit the influence of confounding factors. This is called standardization.

Unfortunately, although standardization increases power, it can induce unrealistically low variability and lead to results that do not generalize to the population of interest. And, in fact, may be irreproducible.

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Standardization fallacy. (read)

Not paying attention to these details and thinking (or hoping) that standardization is always good is the "standardization fallacy". In this column, we look at how standardization can be balanced with heterogenization to avoid this thorny issue.

Voelkl, B., Würbel, H., Krzywinski, M. & Altman, N. (2021) Points of significance: Standardization fallacy. Nature Methods 18:5–6.

Graphical Abstract Design Guidelines

Fri 13-11-2020

Clear, concise, legible and compelling.

Making a scientific graphical abstract? Refer to my practical design guidelines and redesign examples to improve organization, design and clarity of your graphical abstracts.

Martin Krzywinski @MKrzywinski
Graphical Abstract Design Guidelines — Clear, concise, legible and compelling.