Where am I supposed to go? Where was I supposed to know?get lost in questionsmore quotes

# circles: worthwhile

PNAS Cover: Earth BioGenome Project

# visualization + design

The 2022 Pi Day art is a music album “three one four: a number of notes” . It tells stories from the very beginning (314…) to the very (known) end of π (...264) as well as math (Wallis Product) and math jokes (Feynman Point), repetition (nn) and zeroes (null).

# The art of Pi ($\pi$), Phi ($\phi$) and $e$

2021 $\pi$ reminds us that good things grow for those who wait.' edition.
2019 $\pi$ has hundreds of digits, hundreds of languages and a special kids' edition.
2018 $\pi$ day stitches street maps into new destinations.
2017 $\pi$ day imagines the sky in a new way.

2016 $\pi$ approximation day wonders what would happen if about right was right.
2016 $\pi$ day sees digits really fall for each other.
2015 $\pi$ day maps transcendentally.
2014 $\pi$ approx day spirals into roughness.

2014 $\pi$ day hypnotizes you into looking.
2014 $\pi$ day
2013 $\pi$ day is where it started
Circular $\pi$ art and other distractions

Numbers are a lot of fun. They can start conversations—the interesting number paradox is a party favourite: every number must be interesting because the first number that wasn't would be very interesting! Of course, in the wrong company they can just as easily end conversations.

## is π normal?

It is not yet known whether the digits of π are normal—determining this is an important problem in mathematics. In other words, is the distribution of digit frequencies in π uniform? Do each of the digits 0–9 appear exactly 1/10th of the time, does every two-digit string appear exactly 1/100th of the time and so on for every finite-length string1?

1 One interesting finite-length string is the 6-digit Fenyman Point (...999999...) which appears at digit 762 in π. The Feynman Point was the subject of 2014 $\pi$ Day art.

This question can be posed for different representations of π—in different bases. The distribution frequencies of 1/10, 1/100, and so on above refer to the representation of π in base 10. This is the way we're used to seeing numbers. However, if π is encoded as binary (base 2), would all the digits in 11.00100100001111... be normal? The table below shows the first several digits of π in each base from 2 to 16, as well as the natural logarithm base, $e$.

 base, $b$ $\pi_b$ base, $b$ $\pi_b$ 2 11.00100100001111 10 3.14159265358979 3 10.01021101222201 11 3.16150702865A48 4 3.02100333122220 12 3.184809493B9186 5 3.03232214303343 13 3.1AC1049052A2C7 6 3.05033005141512 14 3.1DA75CDA813752 7 3.06636514320361 15 3.21CD1DC46C2B7A 8 3.11037552421026 16 3.243F6A8885A300 $e$ 10.10100202000211 source: virtuescience.com

Because the digits in the numbers are essentially random (this is a conjecture), the essence of the art is based on randomness.

A vexing consequence of π being normal is that, because it is non-terminating, π would contain all patterns. Any word you might think of, encoded into numbers in any way, would appear infinitely many times. The entire works of Shakespeare, too. As well, all his plays in which each sentence is reversed, or has one spelling mistake, or two! In fact, you would eventually find π within π, but only if you have infinite patience.

This is why any attempts to use the digits of $\pi$ to infer meaning about anything is ridiculous. The exact opposite of what you find is also in $\pi$.

#### Stoneham's constant

A number can be normal in one base, but another. For example, Stoneham's constant,

$\alpha_{2,3} = 1/2 + 1/(2^{3^1} 3^1) + 1/(2^{3^2} 3^2) + 1/(2^{3^3} 3^3) + ... + 1/(2^{3^k} 3^k) + ...$

is 0.54188368083150298507... in base 10 and 0.100010101011100011100011100... in base 2.

Stoneham's constant is provably normal in base 2. In some other bases, such 6, Stoneham's constant is provably not normal.

# Anatomy of SARS-Cov-2

Tue 31-05-2022

My poster showing the genome structure and position of mutations on all SARS-CoV-2 variants appears in the March/April 2022 issue of American Scientist.

Deadly Genomes: Genome Structure and Size of Harmful Bacteria and Viruses (zoom)

An accompanying piece breaks down the anatomy of each genome — by gene and ORF, oriented to emphasize relative differences that are caused by mutations.

Deadly Genomes: Genome Structure and Size of Harmful Bacteria and Viruses (zoom)

# Cancer Cell cover

Sat 23-04-2022

My cover design on the 11 April 2022 Cancer Cell issue depicts depicts cellular heterogeneity as a kaleidoscope generated from immunofluorescence staining of the glial and neuronal markers MBP and NeuN (respectively) in a GBM patient-derived explant.

LeBlanc VG et al. Single-cell landscapes of primary glioblastomas and matched explants and cell lines show variable retention of inter- and intratumor heterogeneity (2022) Cancer Cell 40:379–392.E9.

My Cancer Cell kaleidoscope cover (volume 40, issue 4, 11 April 2022). (more)

Browse my gallery of cover designs.

A catalogue of my journal and magazine cover designs. (more)

# Nature Biotechnology cover

Sat 23-04-2022

My cover design on the 4 April 2022 Nature Biotechnology issue is an impression of a phylogenetic tree of over 200 million sequences.

Konno N et al. Deep distributed computing to reconstruct extremely large lineage trees (2022) Nature Biotechnology 40:566–575.

My Nature Biotechnology phylogenetic tree cover (volume 40, issue 4, 4 April 2022). (more)

Browse my gallery of cover designs.

A catalogue of my journal and magazine cover designs. (more)

# Nature cover — Gene Genie

Sat 23-04-2022

My cover design on the 17 March 2022 Nature issue depicts the evolutionary properties of sequences at the extremes of the evolvability spectrum.

Vaishnav ED et al. The evolution, evolvability and engineering of gene regulatory DNA (2022) Nature 603:455–463.

My Nature squiggles cover (volume 603, issue 7901, 17 March 2022). (more)

Browse my gallery of cover designs.

A catalogue of my journal and magazine cover designs. (more)

# Happy 2022 $\pi$ Day—three one four: a number of notes

Mon 14-03-2022

Celebrate $\pi$ Day (March 14th) and finally hear what you've been missing.

“three one four: a number of notes” is a musical exploration of how we think about mathematics and how we feel about mathematics. It tells stories from the very beginning (314…) to the very (known) end of π (...264) as well as math (Wallis Product) and math jokes (Feynman Point), repetition (nn) and zeroes (null).

Listen to $\pi$ in the style of 20th century classical music. (details)

The album is scored for solo piano in the style of 20th century classical music – each piece has a distinct personality, drawn from styles of Boulez, Feldman, Glass, Ligeti, Monk, and Satie.

Each piece is accompanied by a piku (or πku), a poem whose syllable count is determined by a specific sequence of digits from π.

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, 2019 $\pi$ Day, 2020 $\pi$ Day and 2021 $\pi$ Day.

# PNAS Cover — Earth BioGenome Project

Fri 28-01-2022

My design appears on the 25 January 2022 PNAS issue.

My PNAS cover design captures the vision of the Earth BioGenome Project — to sequence everything. (more)

The cover shows a view of Earth that captures the vision of the Earth BioGenome Project — understanding and conserving genetic diversity on a global scale. Continents from the Authagraph projection, which preserves areas and shapes, are represented as a double helix of 32,111 bases. Short sequences of 806 unique species, sequenced as part of EBP-affiliated projects, are mapped onto the double helix of the continent (or ocean) where the species is commonly found. The length of the sequence is the same for each species on a continent (or ocean) and the sequences are separated by short gaps. Individual bases of the sequence are colored by dots. Species appear along the path in alphabetical order (by Latin name) and the first base of the first species is identified by a small black triangle.

Lewin HA et al. The Earth BioGenome Project 2020: Starting the clock. (2022) PNAS 119(4) e2115635118.