Trance opera—Spente le Stellebe dramaticmore quotes

# pi day: exciting

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

# visualization + design

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 2016 Art Posters

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.
2017 $\pi$ day
2016 $\pi$ approximation day
2016 $\pi$ day
2015 $\pi$ day
2014 $\pi$ approx 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 art is generated by running a simulation of gravity in which digits of $\pi$ are each assigned a mass and allowed to collide eand orbit each other.

The mathematical details of the simulation can be found in the code section.

## exploring force of gravity in $\pi$

A simulation starts with taking $n$ digits of $\pi$ and arranging them uniformly around a circle. The mass of each digit, $d_i$ (e.g. 3), is given by $(1+d)^k$ where $k$ is a mass power parameter between 0.01 and 1. For example, if $k=0.42$ then the mass of 3 is $(1+3)^{0.42} = 1.79$.

### collapsing three digits—3.14 collide

The figure below shows the evolution of a simulation with $n=3$ digits and $k=1$. The digits 3 and 4 collide to form the digit $3+4 = 7$ and immediately collides with 1 to form $7+1=8$. With only one mass left in the system, the simulation stops.

The evolution of a simulation of gravity using $n=3$ digits of $\pi$ and the mass power $k=1$. The masses are initialized with zero velocity. (zoom)

### adding initial velocity to each mass

When masses have initial velocities, the patterns quickly start to get interesting. In the figure above, the masses are initalized with zero velocity. As soon as the simulation, each mass immediately starts to move directly towards the center of mass of the other two masses.

When the initial velocity is non-zero, such as in the figure below, the masses don't immediately collapse towards one another. The masses first travel with their initial velocity but immediately the gravitational force imparts acceleration that alters this velocity. In the examples below, only those simulations in which the masses collapsed within a time cutoff are shown.

The evolution of a simulation of gravity using $n=3$ digits of $\pi$ and the mass power $k=1$ in which all masses collapsed. The masses are initialized with a random velocity. (zoom)
The evolution of 16 simulations of gravity using $n=3$ digits of $\pi$ and the mass power $k=1$ in which all masses collapsed. The masses are initialized with a random velocity. (zoom)
The evolution of 49 simulations of gravity using $n=3$ digits of $\pi$ and the mass power $k=1$ in which all masses collapsed. The masses are initialized with a random velocity. (zoom)

## allowing the simulation to evolve

Depending on the initial velocities, some systems collapse very quickly, which doesn't make for interesting patterns.

For example, the simulations above evolved over 100,000 steps and in some cases the masses collapsed within 10,000 steps. In the figure below, I require that the system evolves for at least 15,000 steps before collapsing. Lovely doddles, don't you think?

The evolution of 36 simulations of gravity using $n=3$ digits of $\pi$ and the mass power $k=1$ in which all masses collapsed after a minimum amount of time. The masses are initialized with a random velocity. (zoom)

### exploring ensembles

When a simulation is repeated with different initial conditions, the set of outcomes is called an ensemble.

Below, I repeat the simulation 100 times with $n=3$ and $k=0.2$, each time with slightly different initial velocity. The velocities have their $x$- and $y$-components normally distributed with zero mean and a fixed variance. Each of the four ensembles has its simulations evolve over progressively more time steps: 5,000, 7,500, 10,000, and 20,000.

You can see that with 5,000 steps the masses don't yet have a chance to collide. After 7,500, there have been collisions in a small number of systems. The blue mass corresponds to the 3 colliding with 4 and the green mass to 1 colliding with 4. After 10,000, even more collisions are seen and in 3 cases we see total collapse (all three digits collided). After 20,000,

The evolution of 100 simulations of gravity over total time $t$ using $n=3$ digits of $\pi$ and the mass power $k=0.2$. Within each ensemble, the masses are initialized with a different random velocity in each instance. (zoom)

## varying masses

The value of $k$ greatly impacts the outcome of the simulation. When $k$ is very small, all the digits have essentially the same mass. For example, when $k=0.01$ the 0 has a mass of 1 and 9 has a mass of 1.02.

When $k$ is large, the difference in masses is much greater. For example, for $k=2$ the lightest mass is $(1+0)^2=1$ and the heaviest $(1+9)^2=10$. Because the acceleration of a mass is proportional to the mass that is attracting it, in a pair of masses the light mass will accelerate faster.

## interactive gravity simulator

Use this fun inteactive gravity simulator if you want to drop your own masses and watch them orbit.

VIEW ALL

# 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%).

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.

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.

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.

Circos cake celebrating Reuscher et al. 2018 publication of the Oryza longistaminata genome.

# Optimal experimental design

Tue 31-07-2018
Customize the experiment for the setting instead of adjusting the setting to fit a classical design.

The presence of constraints in experiments, such as sample size restrictions, awkward blocking or disallowed treatment combinations may make using classical designs very difficult or impossible.

Optimal design is a powerful, general purpose alternative for high quality, statistically grounded designs under nonstandard conditions.

Nature Methods Points of Significance column: Optimal experimental design. (read)

We discuss two types of optimal designs (D-optimal and I-optimal) and show how it can be applied to a scenario with sample size and blocking constraints.

Smucker, B., Krzywinski, M. & Altman, N. (2018) Points of significance: Optimal experimental design Nature Methods 15:599–600.

Krzywinski, M., Altman, N. (2014) Points of significance: Two factor designs. Nature Methods 11:1187–1188.

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.

# The Whole Earth Cataloguer

Mon 30-07-2018
All the living things.

An illustration of the Tree of Life, showing some of the key branches.

The tree is drawn as a DNA double helix, with bases colored to encode ribosomal RNA genes from various organisms on the tree.

The circle of life. (read, zoom)

All living things on earth descended from a single organism called LUCA (last universal common ancestor) and inherited LUCA’s genetic code for basic biological functions, such as translating DNA and creating proteins. Constant genetic mutations shuffled and altered this inheritance and added new genetic material—a process that created the diversity of life we see today. The “tree of life” organizes all organisms based on the extent of shuffling and alteration between them. The full tree has millions of branches and every living organism has its own place at one of the leaves in the tree. The simplified tree shown here depicts all three kingdoms of life: bacteria, archaebacteria and eukaryota. For some organisms a grey bar shows when they first appeared in the tree in millions of years (Ma). The double helix winding around the tree encodes highly conserved ribosomal RNA genes from various organisms.

Johnson, H.L. (2018) The Whole Earth Cataloguer, Sactown, Jun/Jul, p. 89

# Why we can't give up this odd way of typing

Mon 30-07-2018
All fingers report to home row.

An article about keyboard layouts and the history and persistence of QWERTY.

My Carpalx keyboard optimization software is mentioned along with my World's Most Difficult Layout: TNWMLC. True typing hell.

TNWMLC requires seriously flexible digits. It’s 87% more difficult than using a standard Qwerty keyboard, according to Martin Krzywinski, who created it (Credit: Ben Nelms). (read)

McDonald, T. (2018) Why we can't give up this odd way of typing, BBC, 25 May 2018.