Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca - contact me Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca on Twitter Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca - Lumondo Photography Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca - Pi Art Martin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca - Hilbertonians - Creatures on the Hilbert CurveMartin Krzywinski / Canada's Michael Smith Genome Sciences Centre / mkweb.bcgsc.ca - Pi Day 2020 - Piku
And she looks like the moon. So close and yet, so far.Future Islandsaim highmore quotes

numbers: fun


Scientific graphical abstracts — design guidelines


visualization + design


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
81 digits of `\pi` as a forest of trees: standard, bat cave and underwater editions. ( BUY ARTWORK )
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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 2021 Art Posters - A forest of `\pi` (a Lindenmayer system)

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
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.

The trees along this city street,
Save for the traffic and the trains,
Would make a sound as thin and sweet
As trees in country lanes.
—Edna St. Vincent Millay (City Trees)


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
768 digits of `\pi` as a forest of trees. Underwater technicolor edition. ( BUY ARTWORK )

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
768 digits of `\pi` as a forest of trees. Scorched technicolor edition. ( BUY ARTWORK )

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
768 digits of `\pi` as a forest of leafless trees. Desolate edition. ( BUY ARTWORK )

Welcome to this year's celebration of `\pi` and mathematics.

The theme this year is flower and flowers—in contrast to last year's understandable downturn in mood.

This year's `\pi` poem City Trees by Edna St. Vincent Millay.

This year's `\pi` day song is Sway by Laleh.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A `\pi` day music video!: Transcendental Tree Map premieres on 2020 Pi Day from Max Cooper's Yearning for the Infinite. Animation by Nick Cobby and myself. Watch live from Barbican Centre.

In past years, I've used the digits to draw a star map, run a gravity simulation draw a star map, draw streets of imagined cities. I even took a stab at waxing poetic.

Play time isn't over. This year, the digits of `\pi` sprout an infinite and irrational forest.

Good things grow for those who wait.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The 2020 Pi Day art celebrates the digits of `\pi` with piku (パイク) —poetry inspired by haiku.
They serve as the form for The Outbreak Poems.

Can you see the digits through the forest?

The digits of `\pi` are shown as a forest. Each tree in the forest represents the digits of `\pi` up to the next 9. The first 10 trees are "grown" from the digit sets 314159, 2653589, 79, 3238462643383279, 50288419, 7169, 39, 9, 3751058209, and 749.

The digits control how the tree grows — but there is also a good amount of botanical variation. Below I outline the growth process — see the methods section for details.

the rules of the forest

branches

The first digit of a tree controls how many branches grow from the trunk of the tree. For example, the first tree's first digit is 3, so you see 3 branches growing from the trunk.

The next digit's branches grow from the end of a branch of the previous digit in left-to-right order. This process continues until all the tree's digits have been used up.


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Each tree grows from a set of consecutive digits sampled from the digits of `\pi` up to the next 9. The first tree, shown here, grows from 314159. Each of the digits determine how many branches grow at each fork in the tree — the branches here are colored by their corresponding digit to illustrate this. Leaves encode the digits in a left-to-right order. The digit 9 spawns a flower on one of the branches of the previous digit.

The branching exception is 0, which terminates the current branch — 0 branches grow!

leaves and flowers

The tree's digits themselves are drawn as circular leaves, color-coded by the digit.

The leaf exception is 9, which causes one of the branches of the previous digit to sprout a flower! The petals of the flower are colored by the digit before the 9 and the center is colored by the digit after the 9, which is on the next tree. This is how the forest propagates.


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The colors of a flower are determined by the first digit of the next tree and the penultimate digit of the current tree. If the current tree only has one digit, then that digit is used.

Leaves are placed at the tips of branches in a left-to-right order — you can "easily" read them off. Additionally, the leaves are distributed within the tree (without disturbing their left-to-right order) to spread them out as much as possible and avoid overlap. This order is deterministic.

The leaf placement exception are the branch set that sprouted the flower. These are not used to grow leaves — the flower needs space!

special cases — the forest's children

The digit subset "09" is very special. By the rules above, since 0 terminates the branch and 9 grows a flower, we get a flower on the ground — the tree doesn't get to grow but (luckily) flowers to propagates to the next tree.

Two or more 9's in a row generate a series of flowers. The digit forest poster ends in 5 flowers — these are the Feynman Flowers — created by the 999999 at digit 762, which is called the Feynman Point in `\pi`.


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
768 digits of `\pi` as a forest of trees. ( BUY ARTWORK )
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!

a digit nature walk

The rules of the forest are complicated. The labels below the trees help you orient yourself in the stream of digits. Flowers on the ground have no label.


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Somewhere in the middle of the `\pi` forest. Feeling lost? Orient yourself with friendly labels.

shhh, the trees are sleeping

When the lights go out, it's harder to tell what's going on.


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
768 digits of `\pi` as a forest of leafless trees. Bat cave edition. ( BUY ARTWORK )

And if you really want a deep dive, check out the underwater edition.


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
768 digits of `\pi` as a forest of trees. Underwater edition. ( BUY ARTWORK )

Sometimes it's cloudy and sad in the forest.


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
768 digits of `\pi` as a forest of leafless trees. Desolate edition. ( BUY ARTWORK )

But it's best to see all the posters to make sure you don't miss anything.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The 2018 Pi Day art celebrates the 30th anniversary of `\pi` day and connects friends stitching road maps from around the world. Pack a sandwich and let's go!

How it started

The first digit set is 314159 and the 3141 can be read off from the colored leaves. Left to right, these are: orange, red, yellow, red. The 5 is immediately before a 9, so it sprouts a flower. The petals are colored by the digit (5 is green) and the center by the first digit of the next tree (2 is dark orange).


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The first 46 digits of `\pi` grow as 8 trees. The double 9 at digit 45 creates a flower.

Some trees are smaller than others. The tree for 79 only has a chance to grow 7 branches from the trunk before sprouting a flower.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The 2017 Pi Day art imagines the digits of Pi as a star catalogue with constellations of extinct animals and plants. The work is featured in the article Pi in the Sky at the Scientific American SA Visual blog.

How it's going

The artwork shows the forest up to the end of the Feynman Point, which is the first 999999 in `\pi`. It happens at digit 762 and ends at digit 768.


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Trees 79 to 90 bring us to the end of the Feynman Point — its 6 9's in a row show up as 5 flowers. The petals of the first Feynman Flower and center of the last Feynman Flower take after surrounding digits.

I'll leave you to work out how the Feynman Point results in 5 Feynman Flowers and why the center of the last flower is a different color.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The 2016 Pi Day art imagines the digits of Pi as physical masses collapsing under gravity and is featured in the articles The Gravity of Pi and The Boundless Beauty of Pi at the Scientific American SA Visual blog.

Deterministic but always changing

There is "random" variation in aspects of a tree, such as branch length, angle, and direction of growth. However, the randomness is deterministic — the identical same forest is always generated.

To achieve this, I used the digits of each tree and its predecessor (all but the first have one) to create a random number generator — a linear congruential generator.

If you stare into the forest long enough, you can see the branches sway and sway away.


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Different combinations of variation can create some funky effects. Here I show the digit forest as imagined underwater, in a desert, in a drought and just hanging out in a bat cave.

The more digits in the tree (and its predecessor) the more "randomness" there is in the output of the generator. Two flowers in a row use "99" as the input to the generator, which is no randomness at all. But the generator from the first tree's "314159" offers lots of variation.

Each aspect of the tree that has variation has its own generator. There's more detail about this in the methods section.

VIEW ALL

news + thoughts

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 mkweb.bcgsc.ca
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 mkweb.bcgsc.ca
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 mkweb.bcgsc.ca
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

Tue 16-03-2021

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 mkweb.bcgsc.ca
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

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 mkweb.bcgsc.ca
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 mkweb.bcgsc.ca
Graphical Abstract Design Guidelines — Clear, concise, legible and compelling.

"This data might give you a migrane"

Tue 06-10-2020

An in-depth look at my process of reacting to a bad figure — how I design a poster and tell data stories.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A poster of high BMI and obesity prevalence for 185 countries.

He said, he said — a word analysis of the 2020 Presidential Debates

Thu 01-10-2020

Building on the method I used to analyze the 2008, 2012 and 2016 U.S. Presidential and Vice Presidential debates, I explore word usagein the 2020 Debates between Donald Trump and Joe Biden.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Analysis of word usage by parts of speech for Trump and Biden reveals insight into each candidate.