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Distractions and amusements, with a sandwich and coffee.

And she looks like the moon. So close and yet, so far.
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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.

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)

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.

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.

They serve as the form for The Outbreak Poems.

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 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.

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

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.

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!

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`.

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.

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

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

Sometimes it's cloudy and sad in the forest.

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

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).

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.

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.

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.

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.

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.

A forest of digits

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

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.

And things can get crazy in the forest.

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.

*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.

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

*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.

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.

*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.

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

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.