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# piet mondrian: fun

UCD Computational and Molecular Biology Symposium, Dublin, Ireland. 1-2 Dec 2016.

# visualization + design

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 2016 Art Posters

2016 $\pi$ day
2015 $\pi$ day
2014 $\pi$ approx day
2014 $\pi$ day
2014 $\pi$ day
2013 $\pi$ day
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.

All art posters are available for purchase.
I take custom requests.

This year's $\pi$ day art collection celebrates not only the digit but also one of the fundamental forces in nature: gravity.

In February of 2016, for the first time, gravitational waves were detected at the Laser Interferometer Gravitational-Wave Observatory (LIGO).

The signal in the detector was sonified—a process by which any data can be encoded into sound to provide hints at patterns and structure that we might otherwise miss—and we finally heard what two black holes sound like. A buzz and chirp.

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

## this year's theme music

All the art was processed while listening to Roses by Coeur de Pirate, a brilliant female French-Canadian songwriter, who sounds like a mix of Patricia Kaas and Lhasa. The lyrics Oublie-moi (Forget me) are fitting with this year's theme of gravity.

Mais laisse-moi tomber, laisse-nous tomber
Laisse la nuit trembler en moi
Laisse-moi tomber, laisse nous tomber
Cette fois

But let me fall, let us fall
Let the night tremble in me
Let me fall, let us fall
This time

## The Einstein-$\pi$ connection

The number $\pi$ appears in the fundamental equation of general relativity, which relates gravity (left side) to energy and momentum (right side).

$R_{\mu \nu} - \tfrac{1}{2} Rg_{\mu\nu} = 8 \pi G T_{\mu \nu}$

The reason why $\pi$ appears has to do with the need to include the surface area of the sphere, $4 \pi r^2$ in the mathematics. This is very nicely described in Sean Carrol's article Einstein and $\pi$.

## The gravity of $\pi$

Let's make the digits of $\pi$ into masses, throw them into space, and watch gravity make them collide and orbit each other. Read about the details of the simulation and look at the posters.

The first 14 digits of $\pi$ generate various orbits as the digits are assigned mass and subject to gravity. (BUY ARTWORK)

As the number of digits is increased, more elaborate patterns arise. Here is one simulation using 100 digits.

Things can get a little crazy with mor digits. Here, 153 digits are used. (BUY ARTWORK)

How about 1000 digits? In this simulation the masses are similar and they all collide within the circle.

The first 1000 digits of $\pi$ collapse into a single mass. (BUY ARTWORK)
The first 3 digits of $\pi$ collapse into a single mass. 49 times. (BUY ARTWORK)

VIEW ALL

# Visualizing Clonal Evolution in Cancer

Thu 02-06-2016

Genomic instability is one of the defining characteristics of cancer and within a tumor, which is an ever-evolving population of cells, there are many genomes. Mutations accumulate and propagate to create subpopulations and these groups of cells, called clones, may respond differently to treatment.

It is now possible to sequence individual cells within a tumor to create a profile of genomes. This profile changes with time, both in the kinds of mutation that are found and in their proportion in the overall population.

Ways to present temporal and phylogenetic evolution of clones in cancer. M Krzywinski (2016) Molecular Cell 62:652-656. (read)

Clone evolution diagrams visualize these data. These diagrams can be qualitative, showing only trends, or quantitative, showing temporal and population changes to scale. In this Molecular Cell forum article I provide guidelines for drawing these diagrams, focusing with how to use color and navigational elements, such as grids, to clarify the relationships between clones.

How to draw clone evolution diagrams better. M Krzywinski (2016) Molecular Cell xxx:xxx-xxx. (read)

I'd like to thank Maia Smith and Cydney Nielsen for assistance in preparing some of the figures in the paper.

Krzywinski, M. (2016) Visualizing Clonal Evolution in Cancer. Mol Cell 62:652-656.

# Binning High-Resolution Data

Wed 01-06-2016

Limitations in print resolution and visual acuity impose limits on data density and detail.

Your printer can print at 1,200 or 2,400 dots per inch. At reading distance, your reader can resolve about 200–300 lines per inch. This large gap—how finely we can print and how well we can see—can create problems when we don't take visual acuity into account.

Nature Methods Points of View column: Binning high-resolution data. (read)

The column provides some guidelines—particularly relevant when showing whole-genome data, where the scale of elements of interest such as genes is below the visual acuity limit—for binning data so that they are represented by elements that can be comfortably discerned.

Krzywinski, M. (2016) Points of view: Binning high-resolution data. Nature Methods 13:463.

# 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.

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).

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.

# 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.

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.

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.

# Typographical posters of bird songs

Mon 28-03-2016

Chirp, chirp, chirp but much better looking.

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 $\\pi$.

1,000 digits of $\pi$ under the influence of gravity. (details)

Some strange things can happen.

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.