Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - contact me Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca on Twitter Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Lumondo Photography Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Pi Art Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Hilbertonians - Creatures on the Hilbert Curve
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circles: engaging


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data visualization + art

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Enjoy colors?
Take a look at my color projects and resources.

Color proportions in country flags

Color proportions in country flags / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
(right) 256 country flags as concentric circles showing the proportions of each color in the flag. (left) Unique flags sorted by similarity.

Country flags are pretty colorful and some are even pretty.

Instead of drawing the flag in a traditional way (yawn...), I wanted to draw it purely based on the color proportions in the flag (yay!). There are lots of ways to do this, such as stacked bars, but I decided to go with concentric circles. A few examples are shown below.

Color proportions in country flags / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Country flags drawn as concentric rings. The width of each ring is proportional to square root of the area of that color in the flag. Only colors that occupy 1% or more of the flag are shown. (zoom)

Once flags are drawn this way, they can be grouped by similarity in the color proportions.

Check out the posters or read about the method below.

Or, download my country flag color catalog to run your own analysis.

sampling flag colors

To determine the proportions of colors in each flag, I started with the collection of all country flags in SVG from Wikipedia. The flags are conveniently named using the countries' ISO 3166-2 code. At the time of this project (21 Mar 2017), this repository contained 312 flags, of which I used 256.

I originally wanted to use the flag-icon-css collection, but ran into problems with it. It had flags in only either 1 × 1 or 4 × 3 aspect ratio, which distorted and clipped many flags. Many flags were also inaccurately drawn and had inconsistent use of colors. For example, in Turkey's flag the red inside the white crescent was slightly different than elsewhere in the flag.


 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Flags of 256 countries and territories drawn as concentric circles representing the proportions of colors in the flag. The flags are labeled with the country's ISO 3166-2 code. (BUY ARTWORK)

I converted the SVG files to high resolution PNG (2,560 pixels in width) and sampled the colors in each flag, keeping only those colors that occupied at least 0.01% of the flag. I apply this cutoff to avoid blends between colors due to anti-aliasing applied in the conversion. When drawing the flags as circles, I only use colors that occupy at least 1% of the flag—this impacts flags that have detailed emblems, such as Belize. I apply some rounding off of the proportions and colors with the same proportion are ordered so that lighter colors (by Lab luminance) are in the center of the circle.

perceptual radius scaling

There are various ways to represent the proportions of the flag colors as concentric rings—in other words, to use symbols of different size to encode area.

The accurate way is to have the area of the ring be proportional to the area of the color on the map. The inaccurate way is to encode the area by the the width of the ring. These two cases are the `k=0.5` and `k=1` columns in the figure below, where `k` is the power in `r = a^k` by which the radius of the ring, `r`, is scaled relative to the area, `a`. A perceptual mapping using `k=0.57` has been suggested by some.

Color proportions in country flags / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The concentric rings can be drawn to be either accurate in area (left, `k=0.5`) or to have their width encode the area (right, `k=1`). The hybrid approach is a mix of these two extremes. (zoom)

My goal here is not to encode the proportions so that they can be read off quantitatively. To find a value of `k`, I drew some flags and looked at their concentric ring representation. For example, with `k=0.57` the Nigerian flag's white center is too large for my eye while for `k=1` it is definitely too small. I liked the proportions for `k=1/\sqrt{2}` but wasn't happy with the fact that flags like France's, which have colors in equal areas, didn't have equal width rings.

In the end I decided on a hybrid approach in which the out radius of color `i` whose area is `a_i` is `r_i = a_i^k + \sum_{j=0}^{i-1} a_j^k` where the colors are sorted so that `a_{i-1} \le a_i`. If I use `k=0.25`, I manage to have flags like France have equal width rings but flags like Nigeria in which the proportions are not equal are closer to the encoding with `k=1/\sqrt{2}`. In this hybrid approach smaller areas, such as the white in the map of Turkey, are exaggerated. Notice that here `k` plays a slightly different role—it's used as the power for each color individually, `\sum a^k`, rather than their sum, `\left({\sum a}\right)^k`.

For the purists this choice of encoding might appear as the crime of the worst sort, representing neither correct (`k=0.5`) nor the conventionally incorrect encoding associated with `k=1`. Think of it this way—I know what rule I'm breaking.

calculating flag similarity

The similarity between two flags is calculated by forming an intersection between the radii positions of the concentric rings of the flags.

Color proportions in country flags / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Example of how flag similarity is calculated using the flags of Ukraine and Sweden. (zoom)

For each intersection, the similarity of colors is determined using `\Delta E`, which is the Euclidian distance of the colors in LCH space. I placed less emphasis on luminance and chroma in the similarity calculation by fist transforming the coordinates to `(\sqrt L,\sqrt C, H)`) before calculating color differences. The similarity score is $$ S = \sum \frac{\Delta r}{\sqrt{\Delta E}} $$

Color pairs with `\Delta E < \Delta E_{min} = 5` are considered the same and have an effective `\Delta E = 1`.

Color proportions in country flags / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The order of flags using different approaches to calculating the similarity score. (zoom)

I explored different cutoffs and combinations of transforming the color coordinates. This process was informed based on how the order of the flags looked to me.

Color proportions in country flags / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Reasonable ordering for some similar flags achieved by optimizing how similarity between flags is calculated. (zoom)

I decided to start the order with Tonga, since it had the highest average similarity score to all other flags in some of my trials. The flag that is most different from other flags, as measured by the average similarity score, is Israel.

Color proportions in country flags / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
(left) Order of flags when starting with Tonga. (right) Order of flags when starting with Israel, which is has the lowest average similarity score of all flags. (zoom)

 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Flags of 256 countries and territories drawn as concentric circles representing the proportions of colors in the flag. Flags are sorted by similarity in color proportion and labeled with the country's ISO 3166-2 code. (BUY ARTWORK)

download files

country flag colors

I couldn't find a list of colors in the flags of countries, so I provide my analysis here. Every country's SVG flag was converted into a 2,560 × 1,920 PNG file (4,915,200 pixels). Colors that occupied at least 0.01% of the pixels are listed in their HEX format, followed by the number of pixels they occupy. The fraction of the flag covered by sampled colors is also shown.

DOWNLOAD

#code img_pixels sampled_pixels fraction_sampled_pixels hex:pixels,hex:pixels,...
...
cm 4366506 4364514 0.999544 FCD116:1513103,007A5E:1456071,CE1126:1395340
cn 4369920 4364756 0.998818 DE2910:4260992,FFDE00:103764
co 4364800 4364800 1.000000 FCD116:2183680,003893:1090560,CE1126:1090560
...

country similarity score

DOWNLOAD

#code1 code2 similarity_score
ad ae 0.0108360578506763
ad af 0.0288161214840692
ad ag 0.0510922121861494
ad ai 0.42746294322472
...
zw ye 0.473278765746989
zw yt 0.238101673130705
zw za 0.810589244643825
zw zm 0.573265751850587
VIEW ALL

news + thoughts

Using Circos in Galaxy Australia Workshop

Thu 20-02-2020

A workshop in using the Circos Galaxy wrapper by Rasche and Hiltemann. Event organized by Australian Biocommons.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Using Circos in Galaxy Australia workshop. (zoom)

Download workshop slides.

Galaxy wrapper training materials, Saskia Hiltemann, Helena Rasche, 2020 Visualisation with Circos (Galaxy Training Materials).

Essence of Data Visualization in Bioinformatics Webinar

Thu 20-02-2020

My webinar on fundamental concepts in data visualization and visual communication of scientific data and concepts. Event organized by Australian Biocommons.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Essence of Data Visualization in Bioinformatics webinar. (zoom)

Download webinar slides.

Markov models — training and evaluation of hidden Markov models

Thu 20-02-2020

With one eye you are looking at the outside world, while with the other you are looking within yourself.
—Amedeo Modigliani

Following up with our Markov Chain column and Hidden Markov model column, this month we look at how Markov models are trained using the example of biased coin.

We introduce the concepts of forward and backward probabilities and explicitly show how they are calculated in the training process using the Baum-Welch algorithm. We also discuss the value of ensemble models and the use of pseudocounts for cases where rare observations are expected but not necessarily seen.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Markov models — training and evaluation of hidden Markov models. (read)

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov models — training and evaluation of hidden Markov models. Nature Methods 17:121–122.

Background reading

Altman, N. & Krzywinski, M. (2019) Points of significance: Hidden Markov models. Nature Methods 16:795–796.

Altman, N. & Krzywinski, M. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.

Genome Sciences Center 20th Anniversary Clothing, Music, Drinks and Art

Tue 28-01-2020

Science. Timeliness. Respect.

Read about the design of the clothing, music, drinks and art for the Genome Sciences Center 20th Anniversary Celebration, held on 15 November 2019.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Luke and Mayia wearing limited edition volunteer t-shirts. The pattern reproduces the human genome with chromosomes as spirals. (zoom)

As part of the celebration and with the help of our engineering team, we framed 48 flow cells from the lab.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Precisely engineered frame mounts of flow cells used to sequence genomes in our laboratory. (zoom)

Each flow cell was accompanied by an interpretive plaque explaining the technology behind the flow cell and the sample information and sequence content.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The plaque at the back of one of the framed Illumina flow cell. This one has sequence from a patient's lymph node diagnosed with Burkitt's lymphoma. (zoom)

Scientific data visualization: Aesthetic for diagrammatic clarity

Mon 13-01-2020

The scientific process works because all its output is empirically constrained.

My chapter from The Aesthetics of Scientific Data Representation, More than Pretty Pictures, in which I discuss the principles of data visualization and connect them to the concept of "quality" introduced by Robert Pirsig in Zen and the Art of Motorcycle Maintenance.

Yearning for the Infinite — Aleph 2

Mon 18-11-2019

Discover Cantor's transfinite numbers through my music video for the Aleph 2 track of Max Cooper's Yearning for the Infinite (album page, event page).

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Yearning for the Infinite, Max Cooper at the Barbican Hall, London. Track Aleph 2. Video by Martin Krzywinski. Photo by Michal Augustini. (more)

I discuss the math behind the video and the system I built to create the video.