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
Twenty — minutes — maybe — more.Naomichoose four words

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

Split Plot Design

Tue 03-03-2015

The split plot design originated in agriculture, where applying some factors on a small scale is more difficult than others. For example, it's harder to cost-effectively irrigate a small piece of land than a large one. These differences are also present in biological experiments. For example, temperature and housing conditions are easier to vary for groups of animals than for individuals.

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

The split plot design is an expansion on the concept of blocking—all split plot designs include at least one randomized complete block design. The split plot design is also useful for cases where one wants to increase the sensitivity in one factor (sub-plot) more than another (whole plot).

Altman, N. & Krzywinski, M. (2015) Points of Significance: Split Plot Design Nature Methods 12:165-166.

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

Color palettes for color blindness

Tue 03-03-2015

In an audience of 8 men and 8 women, chances are 50% that at least one has some degree of color blindness1. When encoding information or designing content, use colors that is color-blind safe.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A 12-color palette safe for color blindness

Points of Significance Column Now Open Access

Tue 10-02-2015

Nature Methods has announced the launch of a new statistics collection for biologists.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column is now open access. (column archive)

As part of that collection, announced that the entire Points of Significance collection is now open access.

This is great news for educators—the column can now be freely distributed in classrooms.

...more about the Points of Significance column

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