Feel the vibe, feel the terror, feel the painMad about you, orchestrally.more quotes
very clickable
visualization + math

# $\pi$ Approximation Day Art Posters

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

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 $\pi$.

There are two kinds of $\pi$ Approximation Day posters, which I created to celebrate the 2014 and 2016 $\pi$ approximation days.

There are two kinds of $\pi$ Approximation Day posters, which I created to celebrate the 2014 and 2016 $\pi$ approximation days.

The first uses the Archimedean spiral for its design, which I've used before for other numerical art. These ones were generated for the 2014 $\pi$ approximation day.

The second—and newer, for the 2016 $\pi$ approximation day—packs warped circles, whose ratio of circumference to average diameter is $22/7$ into what I call $\pi$-approximate circular packing. Perfect circular packing occupies 78.5% of the area—what about approximate packing?

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

# Convolutional neural networks

Thu 17-08-2023

Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry. – Richard Feynman

Following up on our Neural network primer column, this month we explore a different kind of network architecture: a convolutional network.

The convolutional network replaces the hidden layer of a fully connected network (FCN) with one or more filters (a kind of neuron that looks at the input within a narrow window).

Nature Methods Points of Significance column: Convolutional neural networks. (read)

Even through convolutional networks have far fewer neurons that an FCN, they can perform substantially better for certain kinds of problems, such as sequence motif detection.

Derry, A., Krzywinski, M & Altman, N. (2023) Points of significance: Convolutional neural networks. Nature Methods 20:.

### Background reading

Derry, A., Krzywinski, M. & Altman, N. (2023) Points of significance: Neural network primer. Nature Methods 20:165–167.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nature Methods 13:541–542.

# Neural network primer

Tue 10-01-2023

Nature is often hidden, sometimes overcome, seldom extinguished. —Francis Bacon

In the first of a series of columns about neural networks, we introduce them with an intuitive approach that draws from our discussion about logistic regression.

Nature Methods Points of Significance column: Neural network primer. (read)

Simple neural networks are just a chain of linear regressions. And, although neural network models can get very complicated, their essence can be understood in terms of relatively basic principles.

We show how neural network components (neurons) can be arranged in the network and discuss the ideas of hidden layers. Using a simple data set we show how even a 3-neuron neural network can already model relatively complicated data patterns.

Derry, A., Krzywinski, M & Altman, N. (2023) Points of significance: Neural network primer. Nature Methods 20:165–167.

### Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of significance: Logistic regression. Nature Methods 13:541–542.

# Cell Genomics cover

Mon 16-01-2023

Our cover on the 11 January 2023 Cell Genomics issue depicts the process of determining the parent-of-origin using differential methylation of alleles at imprinted regions (iDMRs) is imagined as a circuit.

Designed in collaboration with with Carlos Urzua.

Our Cell Genomics cover depicts parent-of-origin assignment as a circuit (volume 3, issue 1, 11 January 2023). (more)

Akbari, V. et al. Parent-of-origin detection and chromosome-scale haplotyping using long-read DNA methylation sequencing and Strand-seq (2023) Cell Genomics 3(1).

Browse my gallery of cover designs.

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

# Science Advances cover

Thu 05-01-2023

My cover design on the 6 January 2023 Science Advances issue depicts DNA sequencing read translation in high-dimensional space. The image showss 672 bases of sequencing barcodes generated by three different single-cell RNA sequencing platforms were encoded as oriented triangles on the faces of three 7-dimensional cubes.

My Science Advances cover that encodes sequence onto hypercubes (volume 9, issue 1, 6 January 2023). (more)

Kijima, Y. et al. A universal sequencing read interpreter (2023) Science Advances 9.

Browse my gallery of cover designs.

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

# Regression modeling of time-to-event data with censoring

Thu 17-08-2023

If you sit on the sofa for your entire life, you’re running a higher risk of getting heart disease and cancer. —Alex Honnold, American rock climber

In a follow-up to our Survival analysis — time-to-event data and censoring article, we look at how regression can be used to account for additional risk factors in survival analysis.

We explore accelerated failure time regression (AFTR) and the Cox Proportional Hazards model (Cox PH).

Nature Methods Points of Significance column: Regression modeling of time-to-event data with censoring. (read)

Dey, T., Lipsitz, S.R., Cooper, Z., Trinh, Q., Krzywinski, M & Altman, N. (2022) Points of significance: Regression modeling of time-to-event data with censoring. Nature Methods 19:1513–1515.

# Music video for Max Cooper's Ascent

Tue 25-10-2022

My 5-dimensional animation sets the visual stage for Max Cooper's Ascent from the album Unspoken Words. I have previously collaborated with Max on telling a story about infinity for his Yearning for the Infinite album.

I provide a walkthrough the video, describe the animation system I created to generate the frames, and show you all the keyframes

Frame 4897 from the music video of Max Cooper's Asent.

The video recently premiered on YouTube.

Renders of the full scene are available as NFTs.