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pi day: beautiful


Visualizaiton workshop at UBC B.I.G. Research Day. 11 May 2016


visualization + design

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The 2016 Pi Day art imagines the digits of Pi as physical masses collapsing under gravity and is featured in the article The Gravity of Pi at the Scientific American SA Visual blog.

`\pi` Day 2014 Art Posters


Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2016 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2015 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` approx day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2014 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
2013 `\pi` day

Pi Day 2014 Art Poster - Folding the Number Pi
 / 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.

For the 2014 `\pi` day, two styles of posters are available: folded paths and frequency circles.

The folded paths show `\pi` on a path that maximizes adjacent prime digits and were created using a protein-folding algorithm.

The frequency circles colourfully depict the ratio of digits in groupings of 3 or 6. Oh, look, there's the Feynman Point!


Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day 2014 poster | Frequency distribution of digits in Pi for each of 128 6-digit groupings in 10 columns up to the Feynman Point. For each grouping the number of times a digit was seen is proportional to the width of the annulus. (zoom, BUY ARTWORK)

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day 2014 poster | Frequency distribution of digits in Pi for each of 128 3-digit groupings in 12 columns up to the Feynman Point. For each grouping the number of times a digit was seen is proportional to the width of the annulus. (zoom, BUY ARTWORK)

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day 2014 poster | Frequency distribution of digits in Pi for each of 128 3-digit groupings in 16 columns up to the Feynman Point. For each grouping the number of times a digit was seen is proportional to the width of the annulus. This is a very satisfying square layout. (zoom, BUY ARTWORK)

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day 2014 poster | Frequency distribution of digits in Pi for each of 128 3-digit groupings in 16 columns up to the Feynman Point, with the first digit (3) offset to the top left. For each grouping the number of times a digit was seen is proportional to the width of the annulus. This is a very satisfying square layout. (zoom, BUY ARTWORK)

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day 2014 poster | Frequency distribution of digits in Pi for the first 4,988 digits of Pi in groupings of 4. This subset contains the triplets for each digit, the last being 888 at digit 4,985. The layout is 29 columns and 43 rows. The first digit (3) offset to the top left. For each grouping the number of times a digit was seen is proportional to the width of the annulus. The Feynman Point 4(999999)8 is found in the middle of row 7. (zoom, BUY ARTWORK)

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day 2014 poster | Frequency distribution of digits in Pi for the first 4,988 digits of Pi in groupings of 4. This subset contains the triplets for each digit, the last being 888 at digit 4,985. The layout is on an Archimedean spiral, with the the first digit (3) in the center. For each grouping the number of times a digit was seen is proportional to the width of the annulus. (zoom, BUY ARTWORK)

Pi Day 2014 Art Poster - Folding the Number Pi
 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca buy artwork
Pi Day 2014 poster | Frequency distribution of digits in Pi for the first 4,988 digits of Pi in groupings of 4. This subset contains the triplets for each digit, the last being 888 at digit 4,985. The layout is on an Archimedean spiral. For each grouping the number of times a digit was seen is proportional to the width of the annulus. (zoom, BUY ARTWORK)
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news + thoughts

Regression diagnostics

Wed 11-05-2016

Residual plots can be used to validate assumptions about the regression model.

Continuing with our series on regression, we look at how you can identify issues in your regression model.

The difference between the observed value and the model's predicted value is the residual, `r = y_i - \hat{y}_i`, a very useful quantity to identify the effects of outliers and trends in the data that might suggest your model is inadequate.

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

We also discuss normal probability plots (or Q-Q plots) and show how these can be used to check that the residuals are normally distributed, which is one of the assumptions of regression (constant variance being another).

Background reading

Altman, N. & Krzywinski, M. (2016) Points of Significance: Analyzing outliers: Influential or nuisance? Nature Methods 13:281-282.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple Linear Regression Nature Methods 12:999-1000.

...more about the Points of Significance column

Analyzing Outliers: Influential or Nuisance?

Fri 08-04-2016

Some outliers influence the regression fit more than others.

This month our column addresses the effect that outliers have on linear regression.

You may be surprised, but not all outliers have the same influence on the fit (e.g. regression slope) or inference (e.g. confidence or prediction intervals). Outliers with large leverage—points that are far from the sample average—can have a very large effect. On the other hand, if the outlier is close to the sample average, it may not influence the regression slope at all.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of Significance column: Analyzing Outliers: Influential or Nuisance? (read)

Quantities such as Cook's distance and the so-called hat matrix, which defines leverage, are useful in assessing the effect of outliers.

Background reading

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple Linear Regression Nature Methods 12:999-1000.

...more about the Points of Significance column

Typographical posters of bird songs

Mon 28-03-2016

Chirp, chirp, chirp but much better looking.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The song of the Northern Flicker, Black-capped Chickadee, Olive-sided Flycatcher and Red-eyed Vireo. Sweet to the eye and ear. (details)

If you like these, check out my other typographical art posters.

Happy 2016 Pi Day—gravity of `\pi`

Mon 14-03-2016

Celebrate `\\pi` Day (March 14th) with colliding digits in space. This year, I celebrate the detection of gravitational waves at the LIGO lab and simulate the effect of gravity on masses created from the digits of `\\pi`.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
1,000 digits of `\pi` under the influence of gravity. (details)

Some strange things can happen.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
44 digits of `\pi` under the influence of gravity. (details)

The art is featured in the Gravity of Pi article on the Scientific American SA Visual blog.

Check out art from previous years: 2013 `\\pi` Day and 2014 `\\pi` Day and 2015 `\\pi` Day.

Neural Circuit Diagrams

Sun 13-03-2016

Use alignment and consistency to untangle complex circuit diagrams.

This month we apply the ideas presented in our column about drawing pathways to neural circuit diagrams. Neural circuits are networks of cells or regions, typically with a large number of variables, such as cell and neurotransmitter type.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Nature Methods Points of View column: Neural circuit diagrams. (read)

We discuss how to effectively route arrows, how to avoid pitfalls of redundant encoding and suggest ways to encorporate emphasis in the layout.

Hunnicutt, B.J. & Krzywinski, M. (2016) Points of View: Neural circuit diagrams. Nature Methods 13:189.

background reading

Hunnicutt, B.J. & Krzywinski, M. (2016) Points of Viev: Pathways. Nature Methods 13:5.

Wong, B. (2010) Points of Viev: Gestalt principles (part 1). Nature Methods 7:863.

Wong, B. (2010) Points of Viev: Gestalt principles (part 2). Nature Methods 7:941.

...more about the Points of View column

Pathways

Mon 04-01-2016

Apply visual grouping principles to add clarity to information flow in pathway diagrams.

We draw on the Gestalt principles of connection, grouping and enclosure to construct practical guidelines for drawing pathways with a clear layout that maintains hierarchy.

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

We include tips about how to use negative space and align nodes to emphasizxe groups and how to effectively draw curved arrows to clearly show paths.

Hunnicutt, B.J. & Krzywinski, M. (2016) Points of Viev: Pathways. Nature Methods 13:5.

background reading

Wong, B. (2010) Points of Viev: Gestalt principles (part 1). Nature Methods 7:863.

Wong, B. (2010) Points of Viev: Gestalt principles (part 2). Nature Methods 7:941.

...more about the Points of View column