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data visualization + art

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Like algorithms?
Enjoy even more `\\pi` art.

Hola Mundo and Hello `\pi`

Art is science in love.
— E.F. Weisslitz

Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Remix of the cover design of Hola Mundo by Hannah Fry. (zoom)
Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Remix of the cover design of Hola Mundo by Hannah Fry. (zoom)
Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Remix of the cover design of Hola Mundo by Hannah Fry. (zoom)

art and algorithms

Some algorithms connect us and some keep us apart—we need them to remind us what it is to be human and what it is to be a computer.

My cover design for Hannah Fry's Hello World: Being Human in the Age of Algorithms is based on my 2013 `\pi` Day art. The book is published by Blackie Books.

Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Hola Mundo by Hannah Fry. Translation by Francisco J. Ramos Mena. Published by Blackie Books. Cover design by Martin Krzywinski. The front cover of the book shows a network based on the first 1,418 digits of `\pi`. (zoom)
Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Hola Mundo by Hannah Fry. Translation by Francisco J. Ramos Mena. Published by Blackie Books. Cover design by Martin Krzywinski. The back cover of the book shows a network based on the first 837 digits of `\pi`. (zoom)

creating the cover

The cover begins with a 57 × 35 matrix of 1,995 colored circles. Each circle encodes a digit of `\pi`, starting with 3.1415.... Inside each circle is a smaller circle whose color is based on the next digit. The radius of the inner circle is `1/\phi^2` where `1/\phi = 0.618` is the Golden Ratio.

Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The beginning of the cover design. 1,995 colored circles encode digits of `\pi`. (zoom)
Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Each circle has a smaller circle inside it that encodes the next digit. (zoom)

Once the circles are drawn, neighbouring circles that correspond to the same digit are connected with thick lines. The thickness of these lines is `t_0 = 3/(2\phi^2)`, relative to the outer circle radius. Circles that correspond to digits whose difference is `1` or `-1` are connected by a slightly thinner line with thickness `t_1 = t_0/\phi`.

Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Neighbouring identical digits are connected with thick lines. (zoom)
Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Neighbouring digits that are off by 1 are connected by thinner lines. (zoom)

More lines are drawn that connect digits with a larger difference, `|d| > 1`. The thickness for these lines is `t_d = t_0/\phi^{|d|}`. When all differences up to `|d| < 6` are accounted for, we get a pleasant jumble of lines.

Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Neighbouring digits whose difference is greater than one are connected by progressively thinner lines. (zoom)
Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Circles representing the digits of `\pi` with all lines connecting neighbouring digits. (zoom)

To accommodate the title and other text on the cover, the design was generated by avoiding drawing any circles within a certain distance of the text.

This way, the network of digits wraps around the text. In the final design, the front page has 1,418 digits and the back has 878 digits.

Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Hola Mundo by Hannah Fry. Translation by Francisco J. Ramos Mena. Cover design by Martin Krzywinski. (zoom)
Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Hola Mundo by Hannah Fry. Translation by Francisco J. Ramos Mena. Cover design by Martin Krzywinski. (zoom)

cover remixes

just the lines

Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Just the connecting lines. (zoom)
Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Triangle color is the average color of their corners. (zoom)
Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Inner circles punched out. (zoom)
Cover design by Martin Krzywinski of Hola Mundo (Hannah Fry) / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Just the triangles. (zoom)
news + thoughts

How Analyzing Cosmic Nothing Might Explain Everything

Thu 18-01-2024

Huge empty areas of the universe called voids could help solve the greatest mysteries in the cosmos.

My graphic accompanying How Analyzing Cosmic Nothing Might Explain Everything in the January 2024 issue of Scientific American depicts the entire Universe in a two-page spread — full of nothing.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
How Analyzing Cosmic Nothing Might Explain Everything. Text by Michael Lemonick (editor), art direction by Jen Christiansen (Senior Graphics Editor), source: SDSS

The graphic uses the latest data from SDSS 12 and is an update to my Superclusters and Voids poster.

Michael Lemonick (editor) explains on the graphic:

“Regions of relatively empty space called cosmic voids are everywhere in the universe, and scientists believe studying their size, shape and spread across the cosmos could help them understand dark matter, dark energy and other big mysteries.

To use voids in this way, astronomers must map these regions in detail—a project that is just beginning.

Shown here are voids discovered by the Sloan Digital Sky Survey (SDSS), along with a selection of 16 previously named voids. Scientists expect voids to be evenly distributed throughout space—the lack of voids in some regions on the globe simply reflects SDSS’s sky coverage.”

voids

Sofia Contarini, Alice Pisani, Nico Hamaus, Federico Marulli Lauro Moscardini & Marco Baldi (2023) Cosmological Constraints from the BOSS DR12 Void Size Function Astrophysical Journal 953:46.

Nico Hamaus, Alice Pisani, Jin-Ah Choi, Guilhem Lavaux, Benjamin D. Wandelt & Jochen Weller (2020) Journal of Cosmology and Astroparticle Physics 2020:023.

Sloan Digital Sky Survey Data Release 12

constellation figures

Alan MacRobert (Sky & Telescope), Paulina Rowicka/Martin Krzywinski (revisions & Microscopium)

stars

Hoffleit & Warren Jr. (1991) The Bright Star Catalog, 5th Revised Edition (Preliminary Version).

cosmology

H0 = 67.4 km/(Mpc·s), Ωm = 0.315, Ωv = 0.685. Planck collaboration Planck 2018 results. VI. Cosmological parameters (2018).

Error in predictor variables

Tue 02-01-2024

It is the mark of an educated mind to rest satisfied with the degree of precision that the nature of the subject admits and not to seek exactness where only an approximation is possible. —Aristotle

In regression, the predictors are (typically) assumed to have known values that are measured without error.

Practically, however, predictors are often measured with error. This has a profound (but predictable) effect on the estimates of relationships among variables – the so-called “error in variables” problem.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Error in predictor variables. (read)

Error in measuring the predictors is often ignored. In this column, we discuss when ignoring this error is harmless and when it can lead to large bias that can leads us to miss important effects.

Altman, N. & Krzywinski, M. (2024) Points of significance: Error in predictor variables. Nat. Methods 20.

Background reading

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nat. Methods 12:999–1000.

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

Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nat. Methods 16:451–452.

Convolutional neural networks

Tue 02-01-2024

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).

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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 20:1269–1270.

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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.

More details about the design.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A catalogue of my journal and magazine cover designs. (more)
Martin Krzywinski | contact | Canada's Michael Smith Genome Sciences CentreBC Cancer Research CenterBC CancerPHSA
Google whack “vicissitudinal corporealization”
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