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Drive, driven. Gave, given.YelloGive me a number of games.more quotes

c: 2


In Silico Flurries: Computing a world of snow. Scientific American. 23 December 2017


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 Skya> 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

Predicting with confidence and tolerance

Wed 07-11-2018
I abhor averages. I like the individual case. —J.D. Brandeis.

We focus on the important distinction between confidence intervals, typically used to express uncertainty of a sampling statistic such as the mean and, prediction and tolerance intervals, used to make statements about the next value to be drawn from the population.

Confidence intervals provide coverage of a single point—the population mean—with the assurance that the probability of non-coverage is some acceptable value (e.g. 0.05). On the other hand, prediction and tolerance intervals both give information about typical values from the population and the percentage of the population expected to be in the interval. For example, a tolerance interval can be configured to tell us what fraction of sampled values (e.g. 95%) will fall into an interval some fraction of the time (e.g. 95%).

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Predicting with confidence and tolerance. (read)

Altman, N. & Krzywinski, M. (2018) Points of significance: Predicting with confidence and tolerance Nature Methods 15:843–844.

Background reading

Krzywinski, M. & Altman, N. (2013) Points of significance: Importance of being uncertain. Nature Methods 10:809–810.

4-day Circos course

Wed 31-10-2018

A 4-day introductory course on genome data parsing and visualization using Circos. Prepared for the Bioinformatics and Genome Analysis course in Institut Pasteur Tunis, Tunis, Tunisia.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Composite of the kinds of images you will learn to make in this course.

Oryza longistaminata genome cake

Mon 24-09-2018

Data visualization should be informative and, where possible, tasty.

Stefan Reuscher from Bioscience and Biotechnology Center at Nagoya University celebrates a publication with a Circos cake.

The cake shows an overview of a de-novo assembled genome of a wild rice species Oryza longistaminata.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Circos cake celebrating Reuscher et al. 2018 publication of the Oryza longistaminata genome.

Optimal experimental design

Tue 31-07-2018
Customize the experiment for the setting instead of adjusting the setting to fit a classical design.

The presence of constraints in experiments, such as sample size restrictions, awkward blocking or disallowed treatment combinations may make using classical designs very difficult or impossible.

Optimal design is a powerful, general purpose alternative for high quality, statistically grounded designs under nonstandard conditions.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Optimal experimental design. (read)

We discuss two types of optimal designs (D-optimal and I-optimal) and show how it can be applied to a scenario with sample size and blocking constraints.

Smucker, B., Krzywinski, M. & Altman, N. (2018) Points of significance: Optimal experimental design Nature Methods 15:599–600.

Background reading

Krzywinski, M., Altman, N. (2014) Points of significance: Two factor designs. Nature Methods 11:1187–1188.

Krzywinski, M. & Altman, N. (2014) Points of significance: Analysis of variance (ANOVA) and blocking. Nature Methods 11:699–700.

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

The Whole Earth Cataloguer

Mon 30-07-2018
All the living things.

An illustration of the Tree of Life, showing some of the key branches.

The tree is drawn as a DNA double helix, with bases colored to encode ribosomal RNA genes from various organisms on the tree.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The circle of life. (read, zoom)

All living things on earth descended from a single organism called LUCA (last universal common ancestor) and inherited LUCA’s genetic code for basic biological functions, such as translating DNA and creating proteins. Constant genetic mutations shuffled and altered this inheritance and added new genetic material—a process that created the diversity of life we see today. The “tree of life” organizes all organisms based on the extent of shuffling and alteration between them. The full tree has millions of branches and every living organism has its own place at one of the leaves in the tree. The simplified tree shown here depicts all three kingdoms of life: bacteria, archaebacteria and eukaryota. For some organisms a grey bar shows when they first appeared in the tree in millions of years (Ma). The double helix winding around the tree encodes highly conserved ribosomal RNA genes from various organisms.

Johnson, H.L. (2018) The Whole Earth Cataloguer, Sactown, Jun/Jul, p. 89

Why we can't give up this odd way of typing

Mon 30-07-2018
All fingers report to home row.

An article about keyboard layouts and the history and persistence of QWERTY.

My Carpalx keyboard optimization software is mentioned along with my World's Most Difficult Layout: TNWMLC. True typing hell.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
TNWMLC requires seriously flexible digits. It’s 87% more difficult than using a standard Qwerty keyboard, according to Martin Krzywinski, who created it (Credit: Ben Nelms). (read)

McDonald, T. (2018) Why we can't give up this odd way of typing, BBC, 25 May 2018.