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If you like space, you will love this. The 2017 π Day art imagines the digits of π as a star catalogue with constellations of extinct animals and plants. The work is featured in the article Pi in the Sky at the Scientific American SA Visual blog.
If you like space, you'll love my the 12,000 billion light-year map of clusters, superclusters and voids. Find the biggest nothings in Boötes and Eridanus.The largest map there is shows the location of voids and galaxy superclusters in our visible universe.

Sky Constellation Shapes and Resources

from an undefined
create (a place)
an account
of us
— Viorica Hrincu

Having recently drawn a few skycharts (Superclusters & Voids, Sanctuary Project), I was frustrated by the lack of parsable resources for the Constellations. Not being able to find a plain-text parsable definition of the constellation figures proved impossible, I created my own.

Quotes on this page are from my conversation with the folks at Sky & Telescope and IAU.

1 · Who is in charge here?

You might be surprised to learn (I certainly was) that while the International Astronomial Union has a working group on stars names (WGSN), nobody is actually in charge of defining a canonical set of constellation shapes. I know — the horror, the horror.

While the IAU constellation boundaries, constellation names, and star names have 'official' IAU values/names, the lines connecting the stars are subject to the artist.
Eric Mamajek (chair, IAU WG Star Names)

2 · Constellation figures

While the IAU maintains a page of constellation maps, these maps were actually produced at Sky & Telescope magazine by Roger Sinnott, who put out the excellent Pocket Sky Atlas.

“The constellation figures on the IAU set of charts came from Sky & Telescope, where they were designed by Alan MacRobert and have been used in the magazine since the early 1990s. They aren't official in any sense, but Alan did give them a lot of careful thought.”
Roger Sinnott (Sky & Telescope)

The constellation shapes themselves were designed for Sky & Telescope by Alan MacRobert. Alan was influenced by shapes drawn by H.A. Rey in his book Stars: A New Way to See Them but in many cases adjusted them to preserve earlier traditions.

“I'm gratified at how the astronomical world has been gravitating to our constellation figures over the years, starting with the IAU. I put a great deal of thought into them.”
Alan MacRobert (Sky & Telescope)

2.1 · Figures can connect

A figure for a constellation may connect to one or more neighbouring figures. For example, the figure of Carina connects to Puppis and Vela.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
CARINA CONSTELLATION | Carina connects to Vela (via Regor and Alsephina), Puppis (via Canopus) and Pyxis.

2.2 · Connections may have gaps

Some connections terminate short of their endpoint — these gaps were intentionally included by Alan in his original designs. The gaps are indicated by a flag in the figure records and a unit vector along the line is included on either end to help you draw the line short of its end.

In the case of Carina (above), you can see that its connections to the stars of Vela and Puppis have a gap.

Two other examples (of many) are Hydra and Orion.

2.2.1 · Hydra

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
HYDRA CONSTELLATION | In the long serpentine figure of Hydra, there are short gaps around Alpha and Beta Crateris.

“There are other cases, too, when our lines do not quite connect to stars. For example, in the long serpentine figure of Hydra, we intentionally left short gaps around α and β Crateris. That's because those stars officially belong to Crater, rather than Hydra, even though they take part in the geometrical figures of both.”
Roger Sinnott (Sky & Telescope)

2.2.2 · Orion

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
ORION CONSTELLATION | Orion has a raised arm (the single line from α Orionis to μ and the ξ–ν pair) wielding a heavy club (outlined by ξ–ν–χ1–χ2).

“Alan [added gaps] quite consciously, to give the simple geometric figure a shape more like a man with two legs (i.e., like Orion, the Hunter, in mythology). And as a hunter, Orion has a raised arm (the single line from α Orionis to μ and the ξ–ν pair) wielding a heavy club (outlined by ξ–ν–χ1–χ2).
Among the charts there are several other cases of a line going to the rough midpoint of two close stars, because the observer thinks of them as a pair rather than two distinct stars.”
— [Roger Sinnott](https://skyandtelescope.org/about-us/roger-w-sinnott/) (Sky & Telescope)

2.3 · Carina intersects Volans

Connections of figures do not intersect except for the edge case of Carina and Volans. The α–β connection of Carina crosses Volans and intersects its α–β and α–ε connections.

This resolved by introducing a gap in the Carina α–β line.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
VOLANS CONSTELLATION | A line in Carina cuts through Volans.

“I forgot to mention one more situation where a gap occurs in the [figure] of a constellation, at least as implemented in our S&T software. We did not want a line belonging to one constellation to cross or intersect a line of another constellation. The best example (maybe the only example) appears on the attached chart of Volans.”
Roger Sinnott (Sky & Telescope)

The α–β gap is not encoded in my file because its position depends on the projection.

“In our software, we took care of this and other gaps in lines by adding fictitious stars to the database for the lines to end on. These fictitious stars lie on the great circle between the two real stars that define the line. This way, a graphic artist who finalizes a chart does not have to remember to insert needed gaps manually.”
Roger Sinnott (Sky & Telescope)

3 · Conversation with Alan MacRobert

I had a great exchange with Alan about the figures.

Here, he comments about his design philosophy.

Each [figure] is a compromise between competing priorities.
The lines must include the lines that the eye can't help but naturally see. Two bright stars near each other must be connected because that's what the eye does, no escaping it.
Figures should look like the thing named if reasonably possible. I started with H. A. Rey's groundbreaking figures in his constellation guide The Stars, a New Way to See Them (1952).
But Rey committed four sins.
1 — He occasionally fudged star positions slightly to make his figures work better.
2 — He sometimes used stars too faint for most modern skywatchers to see.
3 — He often connected stars with line patterns too complicated for the eye to see easily, while skipping the lines between brighter stars that the eye can't help but see.
4 — And, he paid no attention to the constellations' deep heritage in how they have been oriented and depicted since Greco-Roman times. This often makes them conflict with the representations that were the basis of it all and that are seen throught astronomy literature.
I tried to make realistic stick figures that did match ancient representations, as recorded in the Almagest star names ('foot,' 'knee', 'tail', etc.) and old depictions going back to the Farnese Globe.
Alan MacRobert (Sky & Telescope)

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
VIRGO CONSTELLATION | Virgo is holding the ear of grain (Spica) in one hand and sowing seeds on the springtime fields with her other hand.

3.1 · Virgo

The Virgo I eventually came up with, for instance, not only matches her ancient arrangement but for the first time, as far as I know, matches her activity: holding the ear of grain Spica in one hand and sowing seeds on the springtime fields with her other hand.
I suspect that I rediscovered the original Virgo as seen by farmers and herdsmen outdoors at night before the 'fine arts' took over (starting with the artist hired to paint the constellations on a ceiling in the palace of Philip of Macedon. A king doesn't want grubby shepherds' stick figures, he wants Fine Art to show off. And so it began.)
Alan MacRobert (Sky & Telescope)

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
HERCULES CONSTELLATION | The head, the knee and the club.

3.2 · Hercules

Similarly, I went with the Hercules who has 'Head of the Giant' as his head star, 'Knee' as his knee star, and 'Club' as the top of his club.
This makes Hercules hold out his lion skin in front of him, echoing Orion also waving a club over his head and holding out a lion skin in front of him. I doubt that was a coincidence.
Alan MacRobert (Sky & Telescope)

3.3 · Centaurus and Lupus

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
LUPUS CONSTELLATION | Stabbed in the head by Centaurus' spear.

And I made sure that Lupus is being stabbed in the throat by Centaurus thrusting a spear.
Alan MacRobert (Sky & Telescope)

3.4 · Cassiopea

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
CASSIOPEIA CONSTELLATION | It's a W, no matter what.

But a few just had to be what everybody now sees.
Cassiopeia is a W no matter what — even though her stars, including fainter ones connected in the ancient order by name from head to foot, suggest an evocative profile outline of a grieving woman.
Alan MacRobert (Sky & Telescope)

3.5 · Sagittarius

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca

...and Sagittarius is a teapot, even though H. A. Ray's version is more or less historically correct, bow and arrow and all as far as I could tell.
Alan MacRobert (Sky & Telescope)

4 · Download constellation figures

This file contains all the information you need to draw basic star maps (with name and designation labels) and constellation figures. It is the most complete (and self-contained) sky constellation dataset of its kind — if you find something better, let me know!

To learn more, read the detailed explanation of this file.

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.”


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)


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


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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