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# numbers: beautiful

DNA on 10th — street art, wayfinding and font

# visualization + design

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!

# $\pi$ Approximation Day Art Posters

2019 $\pi$ has hundreds of digits, hundreds of languages and a special kids' edition.
2018 $\pi$ day
2017 $\pi$ day
2016 $\pi$ approximation day
2016 $\pi$ day
2015 $\pi$ day
2014 $\pi$ approx day
2014 $\pi$ day
2013 $\pi$ day
Circular $\pi$ art

The never-repeating digits of $\pi$ can be approximated by $22/7 = 3.142857$ to within 0.04%. These pages artistically and mathematically explore rational approximations to $\pi$. This 22/7 ratio is celebrated each year on July 22nd. If you like hand waving or back-of-envelope mathematics, this day is for you: $\pi$ approximation day!

Want more math + art? Discover the Accidental Similarity Number. Find humor in my poster of the first 2,000 4s of $\pi$.

## art of $\pi$ rational approximation

The poster shows the accuracy of 10,000 rational approximations of $\pi$ for each $m/n$ and $m=1...10000$. Read about the details of the method.

Accuracy of 10,000 rational approximations of $\pi$ for each $m/n$ and $m=1...10000$. (zoom, BUY ARTWORK)

## art of $\pi$-approximate packing

These posters show warped circles, which embody the 22/7 approximation of $\pi$, using a retro 1970's color scheme. Read about the details of the method.

Packing of warped circles that embody the 22/7 approximation of $\pi$. Here warped circles are clipped by perfect circles. The color scheme is 1970's retro. (zoom, BUY ARTWORK)
Packing of warped circles that embody the 22/7 approximation of $\pi$. Here perfect circles are clipped by warped circles. The color scheme is 1970's retro. (zoom, BUY ARTWORK)
Packing of warped circles that embody the 22/7 approximation of $\pi$. Here warped circles are clipped by perfect circles. The color scheme is 1970's retro. (zoom, BUY ARTWORK)
Packing of warped circles that embody the 22/7 approximation of $\pi$. Here perfect circles are clipped by warped circles. The color scheme is 1970's retro. (zoom, BUY ARTWORK)
Packing of warped circles that embody the 22/7 approximation of $\pi$. Here warped circles are clipped by perfect circles. The color scheme is 1970's retro. (zoom, BUY ARTWORK)
Packing of warped circles that embody the 22/7 approximation of $\pi$. Here perfect circles are clipped by warped circles. The color scheme is 1970's retro. (zoom, BUY ARTWORK)
Packing of warped circles that embody the 22/7 approximation of $\pi$. Here warped circles are clipped by perfect circles. The color scheme is 1970's retro. (zoom, BUY ARTWORK)
Packing of warped circles that embody the 22/7 approximation of $\pi$. Here perfect circles are clipped by warped circles. The color scheme is 1970's retro. (zoom, BUY ARTWORK)
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# Genome Sciences Center 20th Anniversary Clothing, Music, Drinks and Art

Wed 22-01-2020

Science. Timeliness. Respect.

Read about the design of the clothing, music, drinks and art for the Genome Sciences Center 20th Anniversary Celebration, held on 15 November 2019.

Luke and Mayia wearing limited edition volunteer t-shirts. The pattern reproduces the human genome with chromosomes as spirals. (zoom)

As part of the celebration and with the help of our engineering team, we framed 48 flow cells from the lab.

Precisely engineered frame mounts of flow cells used to sequence genomes in our laboratory. (zoom)

Each flow cell was accompanied by an interpretive plaque explaining the technology behind the flow cell and the sample information and sequence content.

The plaque at the back of one of the framed Illumina flow cell. This one has sequence from a patient's lymph node diagnosed with Burkitt's lymphoma. (zoom)

# Scientific data visualization: Aesthetic for diagrammatic clarity

Mon 13-01-2020

The scientific process works because all its output is empirically constrained.

My chapter from The Aesthetics of Scientific Data Representation, More than Pretty Pictures, in which I discuss the principles of data visualization and connect them to the concept of "quality" introduced by Robert Pirsig in Zen and the Art of Motorcycle Maintenance.

# Yearning for the Infinite — Aleph 2

Mon 18-11-2019

Discover Cantor's transfinite numbers through my music video for the Aleph 2 track of Max Cooper's Yearning for the Infinite (album page, event page).

Yearning for the Infinite, Max Cooper at the Barbican Hall, London. Track Aleph 2. Video by Martin Krzywinski. Photo by Michal Augustini. (more)

I discuss the math behind the video and the system I built to create the video.

# Hidden Markov Models

Mon 18-11-2019

Everything we see hides another thing, we always want to see what is hidden by what we see.
—Rene Magritte

A Hidden Markov Model extends a Markov chain to have hidden states. Hidden states are used to model aspects of the system that cannot be directly observed and themselves form a Markov chain and each state may emit one or more observed values.

Hidden states in HMMs do not have to have meaning—they can be used to account for measurement errors, compress multi-modal observational data, or to detect unobservable events.

Nature Methods Points of Significance column: Hidden Markov Models. (read)

In this column, we extend the cell growth model from our Markov Chain column to include two hidden states: normal and sedentary.

We show how to calculate forward probabilities that can predict the most likely path through the HMM given an observed sequence.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Hidden Markov Models. Nature Methods 16:795–796.

Altman, N. & Krzywinski, M. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.

# Hola Mundo Cover

Sat 21-09-2019

My cover design for Hola Mundo by Hannah Fry. Published by Blackie Books.

Hola Mundo by Hannah Fry. Cover design is based on my 2013 $\pi$ day art. (read)

Curious how the design was created? Read the full details.

# Markov Chains

Tue 30-07-2019

You can look back there to explain things,
but the explanation disappears.
You'll never find it there.
Things are not explained by the past.
They're explained by what happens now.
—Alan Watts

A Markov chain is a probabilistic model that is used to model how a system changes over time as a series of transitions between states. Each transition is assigned a probability that defines the chance of the system changing from one state to another.

Nature Methods Points of Significance column: Markov Chains. (read)

Together with the states, these transitions probabilities define a stochastic model with the Markov property: transition probabilities only depend on the current state—the future is independent of the past if the present is known.

Once the transition probabilities are defined in matrix form, it is easy to predict the distribution of future states of the system. We cover concepts of aperiodicity, irreducibility, limiting and stationary distributions and absorption.

This column is the first part of a series and pairs particularly well with Alan Watts and Blond:ish.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.