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Twenty — minutes — maybe — more.Naomichoose four wordsmore quotes

DNA on 10th — street art, wayfinding and font


data visualization + art

If you like space, you'll love my 2017 Pi Day art which imagines the digits as a star catalogue. Meet the Quagga and Aurochs—the Constellations in this sky are extinct animals and plants.

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

Sometimes when you stare at the void, the void sends you a poem.

Universe—Superclusters and Voids

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The Universe — Superclustesr and Voids. The two supergalactic hemispheres showing Abell clusters (blue), superclusters (magenta) and voids (black) within a distance of 6,000 million light-years from the Milky Way.

The average density of the universe is about `10 \times 10^{-30} \text{ g/cm}^3` or about 6 protons per cubic meter. This should put some perspective in what we mean when we speak about voids as "underdense regions".

listen: there's a hell
of a good universe next door; let's go
—e.e. cummings (pity this monster, manunkind)

evolution of the universe superclusters and voids poster

Below I describe the design process of the poster, which is available in various color schemes.

The distances on the poster are all light-travel distances. To learn more about how distances are measured in the Universe, I've put together a short tutorial and calculator on space expansion, light-travel and comoving distances.

The reference section links to reading material about the details of individual elements, such as the coordinate system.

inspiration

I was motivated by this map by Richard Powell of the Universe within 2 billion light years.

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
This is a map of all the major known superclusters within two billion light years plotted onto the supergalactic plane. Each point on this map is a rich cluster of galaxies containing hundreds of galaxies as listed in Abell's catalog of rich clusters of galaxies. This map does not show every rich cluster but only those which are grouped together into large supercluster formations. Each of these superclusters must also contain hundreds or maybe thousands of smaller groups of galaxies. This map is clearly not complete, the plane of our galaxy runs approximately down the centre of the map and most astronomers prefer to study galaxies that are far away from this plane where there is a lot less gas and dust obscuring our view of the universe. This explains why most of the known superclusters are on the left and right sides of the map (original caption by Richard Powell).

I started dutifully tracing the map and I got as far as the image below...

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Beginning tracing the map by Richard. (zoom)

...before I decided that I should just parse Richard's list of superclusters and programmatically generate the map.

#Common Name   Equatorial   Supergal Redsh Dis  Size Con     Abell clusters in the
#              Coordinates  Coords   z     Mly  Mly          in the supercluster
#              RA    Dec    L°  B°
Centaurus      13 00 -32.0  148  -7  0.014 194  150  Cen-Hya 1060,3526,3565,3574,3581
Perseus-Pisces 02 32 +39.8  341  -8  0.016 222  100  Per-And 262,347,426
Pavo-Indus     20 34 -37.0  230 +32  0.017 235  100  Ind-Mic 3656,3698,3742
...

You can download a plain-text and tidied version of this file, in which the Abell list for a supercluster is now on a single line.

Below is my first attempt. This is a top-down view of the supergalactic equator. Clusters in the Southern Supergalactic Hemisphere are joined to the equator plane by dotted lines.

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Superclusters projected top-down on the supergalactic equator. (zoom)

I liked the angled view of Richard's map, so I adjusted the code to achieve this.

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Superclusters projected projected on the supergalactic equator. View angle is about 15 degrees. (zoom)

I knew I wanted to draw the voids on the map, so I scraped some coordinates from Wikipedia's List of Voids and added them to the map.

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Superclusters and voids projected on the supergalactic equator. View angle is about 15 degrees. (zoom)

The object on the far left is the Eridanus Void, which is a hypothesized void to explain the CMBR Cold Spot. I wanted this in the map, but the scale made it difficult—Richard's list of clusters only went out as far as about 2.7 billion light-years but The Eridanus Void is between 6 and 10 billion light years away.

To accomodate this void on the map I needed either (a) more superclusters to fill out the map and/or (b) scale the distance with a log (e.g. `log(d)`) or power transformation (e.g. `d^k`).

There was also another issue: my code implemented an erzats 2-dimensional projection, not an actual orthographic or perspective 2d projection.

VizieR astronomical catalogues

For more data, I went to the VizieR database of astronomical catalogues. It's a little clunky but offers a portal to an absolutely immense amount of data. Once you gain familiarity with the interface, it can feel like the Universe is within reach.

I made use of the Abell catalogue and the supercluster catalogue that groups the Abell clusters into superclusters.

VII/110A Rich Clusters of Galaxies, Abell+, 1989

J/MNRAS/445/4073 Two catalogues of superclusters, Chow-Martinez+, 2014

applying an orthographic projection

When these catalogues are plotted using an authentic projection, the result is the map below.

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Superclusters (orange), Abell clusters (blue) and voids (black) from the VizieR catalogues VII/110 and J/MNRAS/445/4073 projected on the supergalactic equator. View angle is 15 degrees. (zoom)

building the poster

When both hemispheres are shown together, there's a lot of overlap between objects close to the equator. To mitigate this, below is my first attempt at separating the hemispheres and building a poster of the map.

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
First draft of a poster of superclusters, Abell clusters and voids. (zoom)

Below is a close crop of a region of the poster. At this point, I'm still using the bitmap Mini 7 Condensed font and including labels for all Abell and superclusters.

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Close up of a region of the early draft of the poster. (zoom)

Each supercluster also has its constellation designation. This tiny detail took a while to work out. The coordinates had to be precessed to 1875 to apply the IAU constellation boundary criteria.

VI/42 Identification of a Constellation From Position, Roman, 1987

adding stars and constellations

To manage the density of the labels—especially the constellation labels—I thought it would be better to simply show the constellations. I thought that the natural place to put the constellations would be the surface of the supergalactic sphere at a sufficient distance from the origin to accommodate all the objects within the sphere.

I threw in the sky's brightest 9,110 stars from the Yale Catalogue of Bright Stars.

V/50 Bright Star Catalogue, 5th Revised Ed., Hoffleit+, 1991

I obtained the list of constellation shapes from Marc van der Sluys' list. For each constellation, this list gives the pairs of stars in the Yale Catalogue of Bright Stars that are connected by the constellation lines.

BSC (Yale Catalogue of Bright Stars) constellation edges. by Marc van der Sluys

However, many of Marc's constellations shapes were not the asterisms sanctioned by the IAU. I therefore corrected all the constellation shapes by manually examining the IAU map and cross-referencing the stars to the Yale Catalogue of Bright Stars. Ugh.

My list of IAU constellation shapes conveniently includes the J2000 right ascension and declination for each stars in the pair, along with their HR index, magnitude and name.

IAU Constellation shapes as edges between BSC stars (Yale Catalogue of Bright Stars) by Martin Krzywinski

For example, Cassiopeia's familiar "W" appears as 4 lines that indicate the connections between HR stars 21-168-264-403-542.

Cas  21  2.294583 59.149722 2.27 bet Caph|bet Cas|11 Cas	        
    168 10.127083 56.537222 2.23 alf Schedar|alf Cas|18 Cas
Cas 168 10.127083 56.537222 2.23 alf Schedar|alf Cas|18 Cas	
    264 14.177083 60.716667 2.47 gam BU 499A|BU 1028|gam Cas|27 Cas
Cas 264 14.177083 60.716667 2.47 gam BU 499A|BU 1028|gam Cas|27 Cas
    403 21.454167 60.235278 2.68 del Ruchbah|BUP 19A|del Cas|37 Cas
Cas 403 21.454167 60.235278 2.68 del Ruchbah|BUP 19A|del Cas|37 Cas
    542 28.598750 63.670000 3.38 eps Segin|eps Cas|45 Cas

For more details about the constellations see my IAU Constellation Shape Resources.

colors, fonts and design choices

At this point, I went with a vibrant magenta background and switch to the Gotham typeface for the text. I also separeated the hemispheres completely, which makes the map look a little like the hemispheres of the brain. And that's ok.

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The constellations and stars from the Yale Catalogue of Bright Stars projected on the supergalactic sphere. (zoom)

Once I dropped the Abell clusters, superclusters and voids into the sphere, it was beginning to look crowded.

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Clusters, superclusters and voids in the North Supergalactic Hemisphere, together with constellations and stars. (zoom)

From the close crop below, you can see that the drop lines for each object are clusttering the space.

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Close crop of clusters, superclusters and voids in the North Supergalactic Hemisphere, together with constellations and stars. (zoom)

I struggled with these drop lines. On one hand, I thought they were very important because they anchored the objects to the equator and thus provided a better sense of the object's position. On the other hand, they added to the busyness of the map. Ultimately I settled on a compromise. An object's drop line would only be drawn if it didn't have a neighbouring object of the same type.

a poetic collaboration

I'm very eager to find ways to combine my work with poetry.

This poster features a poem by Viorica Hrincu. It's about nothingness and the somethingness that can arise from it, if we find it. It appears on the bottom right of the poster. Tucked, but not away.

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

Previously, I've collaborated with Paolo Marcazzan for my 2017 `\pi` Day `\pi` in the Sky poster. There, Paolo contributed "Of Black Body", a poem about thermodynamics, constellations and the truth we might find there. For Paolo, the poem hints at our plight (and flight): "For the earthbound, the questions and concerns remain those of identity, passage, escape from transiency, and slow tempering of hope."

interpretive panels and stories

It's likely that neither the coordinate system nor the elements in this map are familiar to most people. Supergalactic what? And what do you mean comoving isn't the first step in cohabitation?

To make the poster accessible, I started adding panels around the map that explained what is drawn, how to read the map, the coordinate system, what superclusters and voids are. I also threw in a few mythological stories, such as the one about Orion and his dogs and about Eridanus.

Also explained are the difference between light-travel and comoving distance along with small graphs that illustrate these concepts.

Read all the stories on the poster.

Universe - Superclusters and Voids / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Adding stories and interpretive panels to the poster— close to a final version. (zoom)
VIEW ALL

news + thoughts

Quantile regression

Sat 01-06-2019
Quantile regression robustly estimates the typical and extreme values of a response.

Quantile regression explores the effect of one or more predictors on quantiles of the response. It can answer questions such as "What is the weight of 90% of individuals of a given height?"

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Quantile regression. (read)

Unlike in traditional mean regression methods, no assumptions about the distribution of the response are required, which makes it practical, robust and amenable to skewed distributions.

Quantile regression is also very useful when extremes are interesting or when the response variance varies with the predictors.

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

Background reading

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

Analyzing outliers: Robust methods to the rescue

Sat 30-03-2019
Robust regression generates more reliable estimates by detecting and downweighting outliers.

Outliers can degrade the fit of linear regression models when the estimation is performed using the ordinary least squares. The impact of outliers can be mitigated with methods that provide robust inference and greater reliability in the presence of anomalous values.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Analyzing outliers: Robust methods to the rescue. (read)

We discuss MM-estimation and show how it can be used to keep your fitting sane and reliable.

Greco, L., Luta, G., Krzywinski, M. & Altman, N. (2019) Points of significance: Analyzing outliers: Robust methods to the rescue. Nature Methods 16:275–276.

Background reading

Altman, N. & Krzywinski, M. (2016) Points of significance: Analyzing outliers: Influential or nuisance. Nature Methods 13:281–282.

Two-level factorial experiments

Fri 22-03-2019
To find which experimental factors have an effect, simultaneously examine the difference between the high and low levels of each.

Two-level factorial experiments, in which all combinations of multiple factor levels are used, efficiently estimate factor effects and detect interactions—desirable statistical qualities that can provide deep insight into a system.

They offer two benefits over the widely used one-factor-at-a-time (OFAT) experiments: efficiency and ability to detect interactions.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Two-level factorial experiments. (read)

Since the number of factor combinations can quickly increase, one approach is to model only some of the factorial effects using empirically-validated assumptions of effect sparsity and effect hierarchy. Effect sparsity tells us that in factorial experiments most of the factorial terms are likely to be unimportant. Effect hierarchy tells us that low-order terms (e.g. main effects) tend to be larger than higher-order terms (e.g. two-factor or three-factor interactions).

Smucker, B., Krzywinski, M. & Altman, N. (2019) Points of significance: Two-level factorial experiments Nature Methods 16:211–212.

Background reading

Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments.. Nature Methods 11:597–598.

Happy 2019 `\pi` Day—
Digits, internationally

Tue 12-03-2019

Celebrate `\pi` Day (March 14th) and set out on an exploration explore accents unknown (to you)!

This year is purely typographical, with something for everyone. Hundreds of digits and hundreds of languages.

A special kids' edition merges math with color and fat fonts.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
116 digits in 64 languages. (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
223 digits in 102 languages. (details)

Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day, 2017 `\pi` Day and 2018 `\pi` Day.

Tree of Emotional Life

Sun 17-02-2019

One moment you're :) and the next you're :-.

Make sense of it all with my Tree of Emotional life—a hierarchical account of how we feel.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A section of the Tree of Emotional Life.

Find and snap to colors in an image

Sat 29-12-2018

One of my color tools, the colorsnap application snaps colors in an image to a set of reference colors and reports their proportion.

Below is Times Square rendered using the colors of the MTA subway lines.


Colors used by the New York MTA subway lines.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Times Square in New York City.
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Times Square in New York City rendered using colors of the MTA subway lines.
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Granger rainbow snapped to subway lines colors from four cities. (zoom)