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π Day 2025 Art Posters - TTCAGT: a sequence of digits
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
2025 π DAY | TTCAGT: A sequence of digits. 768 digits of `\pi` as a Sanger sequencing trace of 1,536 peaks. Decode the sequence (BUY ARTWORK)

`\pi` Day 2021 Art Posters - A forest of `\pi` (a Lindenmayer system)


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2024 π DAY | Explore the garden of digits.

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2023 π DAY | Repeated sequence

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2022 π DAY | three one four: a number of digits

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2021 π DAY | Good things grow for those who wait.' edition.


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2020 π DAY | The piku.

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2019 π DAY | Hundreds of digits, hundreds of languages and a special kids' edition.

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2018 π DAY | Street maps to new destinations.

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2017 π DAY | Imagine the sky in a new way.


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 π APPROXIMATION DAY | What would happen if about right was right.

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 π DAY | These digits really fall for each other.

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 π DAY | A transcendental experience.

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 π APPROXIMATION DAY | Spirals into roughness.


`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 π DAY | Hypnotizes you into looking.

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 π DAY | Come into the fold.

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 π DAY | Where it started.

`\pi` Day 2021 Art Posters - A forest of Pi (a Lindenmayer system)
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
CIRCULAR π 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.

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.

The 2015 π Day art takes a Mondrain perspective on π. The art was used in a collaboration with Max Cooper for his track Transcendental Tree Map from the album Yearning for the Infinite. Animation by Nick Cobby and myself. Watch the full show at the 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.

The 2020 π Day art celebrates the digits of π with piku (パイク) — poetry inspired by haiku. They serve as the form for The Outbreak Poems. On our 2022 Pi Day album "three one four: a number of notes", a piku accompanies each track.

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)
The 2019 π Day art celebrates digits of π 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.

The 2018 π Day art celebrates the 30th anniversary of π 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.

If you like space, you will love this. The 2017 π Day art imagines the digits of π 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.

The 2016 π 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](http://blogs.scientificamerican.com/sa-visual.

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.

news + thoughts

Happy 2025 π Day—
TTCAGT: a sequence of digits

Thu 13-03-2025

Celebrate π Day (March 14th) and sequence digits like its 1999. Let's call some peaks.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2025 π DAY | TTCAGT: a sequence of digits. The digits of π are encoded into DNA sequence and visualized with Sanger sequencing. (details)

Crafting 10 Years of Statistics Explanations: Points of Significance

Sun 09-03-2025

I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player

Points of Significance is an ongoing series of short articles about statistics in Nature Methods that started in 2013. Its aim is to provide clear explanations of essential concepts in statistics for a nonspecialist audience. The articles favor heuristic explanations and make extensive use of simulated examples and graphical explanations, while maintaining mathematical rigor.

Topics range from basic, but often misunderstood, such as uncertainty and P-values, to relatively advanced, but often neglected, such as the error-in-variables problem and the curse of dimensionality. More recent articles have focused on timely topics such as modeling of epidemics, machine learning, and neural networks.

In this article, we discuss the evolution of topics and details behind some of the story arcs, our approach to crafting statistical explanations and narratives, and our use of figures and numerical simulations as props for building understanding.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Crafting 10 Years of Statistics Explanations: Points of Significance. (read)

Altman, N. & Krzywinski, M. (2025) Crafting 10 Years of Statistics Explanations: Points of Significance. Annual Review of Statistics and Its Application 12:69–87.

Propensity score matching

Mon 16-09-2024

I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player

In many experimental designs, we need to keep in mind the possibility of confounding variables, which may give rise to bias in the estimate of the treatment effect.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Propensity score matching. (read)

If the control and experimental groups aren't matched (or, roughly, similar enough), this bias can arise.

Sometimes this can be dealt with by randomizing, which on average can balance this effect out. When randomization is not possible, propensity score matching is an excellent strategy to match control and experimental groups.

Kurz, C.F., Krzywinski, M. & Altman, N. (2024) Points of significance: Propensity score matching. Nat. Methods 21:1770–1772.

Understanding p-values and significance

Tue 24-09-2024

P-values combined with estimates of effect size are used to assess the importance of experimental results. However, their interpretation can be invalidated by selection bias when testing multiple hypotheses, fitting multiple models or even informally selecting results that seem interesting after observing the data.

We offer an introduction to principled uses of p-values (targeted at the non-specialist) and identify questionable practices to be avoided.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Understanding p-values and significance. (read)

Altman, N. & Krzywinski, M. (2024) Understanding p-values and significance. Laboratory Animals 58:443–446.

Depicting variability and uncertainty using intervals and error bars

Thu 05-09-2024

Variability is inherent in most biological systems due to differences among members of the population. Two types of variation are commonly observed in studies: differences among samples and the “error” in estimating a population parameter (e.g. mean) from a sample. While these concepts are fundamentally very different, the associated variation is often expressed using similar notation—an interval that represents a range of values with a lower and upper bound.

In this article we discuss how common intervals are used (and misused).

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Depicting variability and uncertainty using intervals and error bars. (read)

Altman, N. & Krzywinski, M. (2024) Depicting variability and uncertainty using intervals and error bars. Laboratory Animals 58:453–456.

Nasa to send our human genome discs to the Moon

Sat 23-03-2024

We'd like to say a ‘cosmic hello’: mathematics, culture, palaeontology, art and science, and ... human genomes.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
SANCTUARY PROJECT | A cosmic hello of art, science, and genomes. (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
SANCTUARY PROJECT | Benoit Faiveley, founder of the Sanctuary project gives the Sanctuary disc a visual check at CEA LeQ Grenoble (image: Vincent Thomas). (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
SANCTUARY PROJECT | Sanctuary team examines the Life disc at INRIA Paris Saclay (image: Benedict Redgrove) (details)
Martin Krzywinski | contact | Canada's Michael Smith Genome Sciences CentreBC Cancer Research CenterBC CancerPHSA
Google whack “vicissitudinal corporealization”
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