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 - Hilbertonians - Creatures on the Hilbert Curve
Poetry is just the evidence of life. If your life is burning well, poetry is just the ashLeonard Cohenwatch

numbers: fun


More than Pretty Pictures—Aesthetics of Data Representation, Denmark, April 13–16, 2015


visualization + design

Typography geek? If you like the geometry and mathematics of these posters, you may enjoy something more lettered. Visions of type: Type Peep Show: The Private Curves of Letters posters.

← art(π,φ,e)

2013 Pi Day Art Posters — March 14

download

numbers.tgz
1,000,000 digits of π, φ, e and ASN.

watch video

Watch the video at Numberphile about my art.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Numberphile video — Pi is Beautiful. (watch)

2014 Pi Day art

Explore Pi Day art for 2014.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Pi Day art for 2014. (explore)

buy artwork

All the artwork can be purchased from Fine Art America.

buy Pi day posters

buy Love in Pi posters

transcend, don't repeat, yourself

Proclus got it right when he said (as quoted by M. Kline in Mathematical Thought from Ancient to Modern Times)

Wherever there is number, there is beauty.

So let's explore what Pi looks like with something whimsical and pretty and colourful. Rational art of the highly irrational, a regime where beauty runs with her hair down and lets her "ribbons to flow confusedly." Robert Herrick says it well in Sweet Disorder,

I see a wild civility;—
Do more bewitch me, than when art
Is too precise in every part.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Each digit is represented by a dot of a different color. The inner grey dots appear to glimmer—this is the luminance effect in action.

The posters explore the relationship between adjacent digits in Pi, which are encoded by color using the scheme shown above. The design appears to shimmer due to the luminance effect. In some versions of the poster, adjacent identical (or similar) digits are connected by lines.

Want more math + art? Discover the Accidental Similarity Number and other number art. Find humor in my poster of the first 2,000 4s of Pi.

The recipe for each poster is included and gives the color of the ith outer/inner circle. π[i] is used to represent the ith digit of π. For example, the recipe

π[i] / π[i+1]

generates a poster whose outer circle color encodes the ith digit and the inner circle color encodes the next digit (i+1). In this scheme, inner and outer circles of adjacent positions have the same color.

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

source and methods

The posters were generated automatically with a Perl script that generated SVG files. Post processing and layout was done in Illustrator. If you are interested in depicting your favourite number this way, let me know.

The design was inspired by the beautiful AIDS posters by Elena Miska.

love in Pi—you can find it here

I calculated Pi to 13,099,586 digits and then I found love.

It's fun to look for words in Pi. I wanted to know the first time that love appears in Pi. When encoded using the scheme a=0, b=1, ..., z=25, love is the digit 1114214. This digit appears first at position 13,099,586 (...892199163111142148187311392...). And, of course, infinitely many times after that.

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)
Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)
Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

If you use the scheme a=1, b=2, ..., z=26, then love becomes 1215225. This is first seen at 6,317,696 (...610311912912152256606850141...).

Because the digits of Pi never repeat and are distributed randomly (as far as we know), if you look long enough you'll find all the words in Pi infinitely many times.

700 digits (20 x 35)

π[i] / grey, 80% opacity

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1], 80% opacity

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

2,800 (40 x 70) digits

π[i] / grey, 80% opacity (equal neighbours connected)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1], 80% opacity (equal neighbours connected)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

— / π[i+1] (equal neighbours connected, unconnected digits not shown)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1] (equal neighbours connected with line width proportional to difference in neighbour digits d∈{0,1,2}, unconnected digits not shown)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1] (equal neighbours connected with line width proportional to difference in neighbour digits d∈{0..5}, unconnected digits not shown)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

Pi (π): — / red (equal neighbours connected, unconnected digits not shown)
Phi (φ): — / white (equal neighbours connected, unconnected digits not shown)
e: — / grey (equal neighbours connected, unconnected digits not shown)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

11,400 (80 x 140) digits

π[i] / grey, 80% opacity (equal neighbours connected)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1], 80% opacity (equal neighbours connected)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1] &>

π[i] / grey, 80% opacity (equal neighbours connected, unconnected digits not shown)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

π[i] / π[i+1], 80% opacity (equal neighbours connected, unconnected digits not shown)

Pi Day Art Poster / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day Art Poster | March 14th is Pi Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

news + thoughts

Before and After—Designing Tiny Figures for Nature Methods

Tue 13-01-2015

I've posted a writeup about the design and redesign process behind the figures in our Nature Methods Points of Significance column.

I have selected several figures from our past columns and show how they evolved from their draft to published versions.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Fig 2 from Points of Significance: Nested designs. (Krzywinski, M. & Altman, N. (2014) Nature Methods 11:977-978.) (...more)

Clarity, concision and space constraints—we have only 3.4" of horizontal space— all have to be balanced for a figure to be effective.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Fig 2c (excerpt) from Points of Significance: Designing comparative experiments. (Krzywinski, M. & Altman, N. (2014) Nature Methods 11:597-598.) (...more)

It's nearly impossible to find case studies of scientific articles (or figures) through the editing and review process. Nobody wants to show their drafts. With this writeup I hope to add to this space and encourage others to reveal their process. Students love this. See whether you agree with my decisions!

Sources of Variation

Thu 08-01-2015

Past columns have described experimental designs that mitigate the effect of variation: random assignment, blocking and replication.

The goal of these designs is to observe a reproducible effect that can be due only to the treatment, avoiding confounding and bias. Simultaneously, to sample enough variability to estimate how much we expect the effect to differ if the measurements are repeated with similar but not identical samples (replicates).

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

We need to distinguish between sources of variation that are nuisance factors in our goal to measure mean biological effects from those that are required to assess how much effects vary in the population.

Altman, N. & Krzywinski, M. (2014) Points of Significance: Two Factor Designs Nature Methods 11:5-6.

Background reading

1. Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.

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

3. Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.

...more about the Points of Significance column

Two Factor Designs

Tue 09-12-2014

We've previously written about how to analyze the impact of one variable in our ANOVA column. Complex biological systems are rarely so obliging—multiple experimental factors interact and producing effects.

ANOVA is a natural way to analyze multiple factors. It can incorporate the possibility that the factors interact—the effect of one factor depends on the level of another factor. For example, the potency of a drug may depend on the subject's diet.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Two Factor Designs. (read)

We can increase the power of the analysis by allowing for interaction, as well as by blocking.

Krzywinski, M., Altman, (2014) Points of Significance: Two Factor Designs Nature Methods 11:1187-1188.

Background reading

Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.

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.

...more about the Points of Significance column

Nested Designs—Assessing Sources of Noise

Mon 29-09-2014

Sources of noise in experiments can be mitigated and assessed by nested designs. This kind of experimental design naturally models replication, which was the topic of last month's column.

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

Nested designs are appropriate when we want to use the data derived from experimental subjects to make general statements about populations. In this case, the subjects are random factors in the experiment, in contrast to fixed factors, such as we've seen previously.

In ANOVA analysis, random factors provide information about the amount of noise contributed by each factor. This is different from inferences made about fixed factors, which typically deal with a change in mean. Using the F-test, we can determine whether each layer of replication (e.g. animal, tissue, cell) contributes additional variation to the overall measurement.

Krzywinski, M., Altman, N. & Blainey, P. (2014) Points of Significance: Nested designs Nature Methods 11:977-978.

Background reading

Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.

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.

...more about the Points of Significance column

Replication—Quality over Quantity

Tue 02-09-2014

It's fitting that the column published just before Labor day weekend is all about how to best allocate labor.

Replication is used to decrease the impact of variability from parts of the experiment that contribute noise. For example, we might measure data from more than one mouse to attempt to generalize over all mice.

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

It's important to distinguish technical replicates, which attempt to capture the noise in our measuring apparatus, from biological replicates, which capture biological variation. The former give us no information about biological variation and cannot be used to directly make biological inferences. To do so is to commit pseudoreplication. Technical replicates are useful to reduce the noise so that we have a better chance to detect a biologically meaningful signal.

Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.

Background reading

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.

...more about the Points of Significance column

Monkeys on a Hilbert Curve—Scientific American Graphic

Tue 19-08-2014

I was commissioned by Scientific American to create an information graphic that showed how our genomes are more similar to those of the chimp and bonobo than to the gorilla.

I had about 5 x 5 inches of print space to work with. For 4 genomes? No problem. Bring out the Hilbert curve!

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Our genomes are much more similar to the chimp and bonobo than to the gorilla. And, we're practically still Denisovans. (details)

To accompany the piece, I will be posting to the Scientific American blog about the process of creating the figure. And to emphasize that the genome is not a blueprint!

As part of this project, I created some Hilbert curve art pieces. And while exploring, found thousands of Hilbertonians!