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
Poetry is just the evidence of life. If your life is burning well, poetry is just the ashLeonard Cohenburn somethingmore quotes

bauhaus: fun


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


visualization + design

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The 2018 Pi Day art celebrates the 30th anniversary of `\pi` day and connects friends stitching road maps from around the world. Pack a sandwich and let's go!

`\pi` Day 2015 Art Posters


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2018 `\pi` day shrinks the world and celebrates road trips by stitching streets from around the world together. In this version, we look at the boonies, burbs and boutique of `\pi` by drawing progressively denser patches of streets. Let's go places.

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2017 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` approximation day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` approx day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 `\pi` day

Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Circular `\pi` art

On March 14th celebrate `\pi` Day. Hug `\pi`—find a way to do it.

For those who favour `\tau=2\pi` will have to postpone celebrations until July 26th. That's what you get for thinking that `\pi` is wrong.

If you're not into details, you may opt to party on July 22nd, which is `\pi` approximation day (`\pi` ≈ 22/7). It's 20% more accurate that the official `\pi` day!

Finally, if you believe that `\pi = 3`, you should read why `\pi` is not equal to 3.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
All art posters are available for purchase.
I take custom requests.

Not a circle in sight in the 2015 `\pi` day art. Try to figure out how up to 612,330 digits are encoded before reading about the method. `\pi`'s transcendental friends `\phi` and `e` are there too—golden and natural. Get it?

This year's `\pi` day is particularly special. The digits of time specify a precise time if the date is encoded in North American day-month-year convention: 3-14-15 9:26:53.

The art has been featured in Ana Swanson's Wonkblog article at the Washington Post—10 Stunning Images Show The Beauty Hidden in `\pi`.

We begin with a square and progressively divide it. At each stage, the digit in `pi` is used to determine how many lines are used in the division. The thickness of the lines used for the divisions can be attenuated for higher levels to give the treemap some texture.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Representing a number using a tree map. Each digit of the number is used to successively divide a shape, such as a square. (zoom)

This method of encoding data is known as treemapping. Typically, it is used to encode hierarchical information, such as hard disk spac usage, where the divisions correspond to the total size of files within directories.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
At each level of the tree map, more digits are encoded. Shown here are tree maps for `pi` for the first 6 levels of division. (zoom)

This kind of treemap can be made from any number. Below I show 6 level maps for `pi`, `phi` (Golden ratio) and `e` (base of natural logarithm).


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
At each level of the tree map, more digits are encoded. Shown here are tree maps for `pi` for the first 6 levels of division. (zoom)

The number of digits per level, `n_i` and total digits, `N_i` in the tree map for `pi`, `phi` and `e` is shown below for levels `i = 1 .. 6`.

           PI             PHI              e
i     n_i    N_i      n_i    N_i      n_i    N_i
1       1      1        1      1        1      1
2       4      5        2      3        3      4
3      15     20        9     12       19     23
4      98    118       59     71       96    119
5     548    666      330    401      574    693
6    2962   3628     1857   2258     3162   3855
7   16616  20244    10041  12299    17541  21396
8   91225 111469
9  500861 612330

Dividing the map

In all the treemaps above, the divisions were made uniformly for each rectangle. With uniform division, the lines that divide a shape are evenly spaced. With randomized division, the placement of lines is randomized, while still ensuring that lines do not coincide.

A multiplier, such as `phi` (Golden Ratio), can be used to control the division. In this case, the first division is made at 1/`phi` (0.62/0.38 split) and the remaining rectangle (0.38) is further divided at `/`phi` (0.24/0.14 split).


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom)

Using a non-uniform multipler is one way to embed another number in the art.

When a multiplier like `phi` is used, divisions at the top levels create very large rectangles. To attenuate this, the effect of the multiplier can be weighted by the level. Regardless of what multiplier is used, the first level is always uniformly divided. Division at subsequent levels incorporates more of the multiplier effect.

The orientation of the division can be uniform (same for a layer and alternating across layers), alternating (alternating across and within a layer) or random. This modification has an effect only if the divisions are not uniform.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom)

Adjusting line thickness

To emphasize the layers, a different line thickness can be used. When lines are drawn progressively thinner with each layer, detail is controlled and the map has more texture.

When all lines have the same thickness, it is harder to distinguish levels.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom)

You could see this as a challenge! Below I show the treemaps for `pi`, `phi` and `e` with and without stroke modulation.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom)

When displayed at a low resolution (the image below is 620 pixels across), shapes at higher levels appear darker because the distance between the lines within is close to (or smaller) than a pixel. By matching the line thickness to the image resolution, you can control how dark the smallest divisions appear.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom)

Adding color

Adding color can make things better, or worse. Dropping color randomly, without respect for the level structure of the treemap, creates a mess.

We can rescue things by increasing the probability that a given rectangle will be made transparent—this will allow the color of the rectangle below to show through. Additionally, by drawing the layers in increasing order, smaller rectangles are drawn on top of bigger ones, giving a sense of recursive subdivision.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The divisions of each shape can be influenced by another number and the level at which the division is performed. (zoom)

Because the color is assigned randomly, various instances of the treemap can be made. The maps below have the same proportion of colors and transparency (same as the first image in second row in the figure above) and vary only by the random seed to pick colors.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Different instances of 5 level `pi` treemaps. The proportion of transparent, white, yellow, red and blue shapes is 20:1:1:1:1. (zoom)

Coloring using adjacency graph

The color assignments above were random. For each shape the probability of choosing a given color (transparent, white, yellow, red, blue) was the same.

Color choice for a shape can also be influenced by the color of neighbouring shapes. To do this, we need to create a graph that captures the adjacency relationship between all the shapes at each level. Below I show the first 4 levels of the `pi` treemap and their adjacency graphs. In each graph, the node corresponds to a shape and an edge between nodes indicates that the shapes share a part of their edge. Shapes that touch only at a corner are not considered adjacent.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Different instances of 5 level `pi` treemaps. The proportion of transparent, white, yellow, red and blue shapes is 20:1:1:1:1. (zoom)

One way in which the graphs can be used is to attempt to color each layer using at most 4 colors. The 4 color theorem tells us that only 4 unique colors are required to color maps such as these in a way that no two neighbouring shapes have the same color.

It turns out that the full algorithm of coloring a map with only 4 colors is complicated, but reasonably simple options exist.. For the maps here, I used the DSATUR (maximum degree of saturation) approach.


Pi Day 2015 Art Posters
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Different instances of 5 level `pi` treemaps. The proportion of transparent, white, yellow, red and blue shapes is 20:1:1:1:1. (zoom)

The DSATUR algorithm works well, but does not guarantee a 4-color solution. It performs no backtracking. If you look carefully, one of the rectangles in the 4th layer (top right quadrant in the graph) required a 5th color (shown black).

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news + thoughts

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)

Take your medicine ... now

Wed 19-12-2018

Drugs could be more effective if taken when the genetic proteins they target are most active.

Design tip: rediscover CMYK primaries.

More of my American Scientific Graphic Science designs

Ruben et al. A database of tissue-specific rhythmically expressed human genes has potential applications in circadian medicine Science Translational Medicine 10 Issue 458, eaat8806.

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.