Poetry is just the evidence of life. If your life is burning well, poetry is just the ashburn somethingmore quotes

# numbers: beautiful

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!

# The art of Pi ($\pi$), Phi ($\phi$) and $e$

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

Numbers are a lot of fun. They can start conversations—the interesting number paradox is a party favourite: every number must be interesting because the first number that wasn't would be very interesting! Of course, in the wrong company they can just as easily end conversations.

## is π normal?

It is not yet known whether the digits of π are normal—determining this is an important problem in mathematics. In other words, is the distribution of digit frequencies in π uniform? Do each of the digits 0–9 appear exactly 1/10th of the time, does every two-digit string appear exactly 1/100th of the time and so on for every finite-length string1?

1 One interesting finite-length string is the 6-digit Fenyman Point (...999999...) which appears at digit 762 in π. The Feynman Point was the subject of 2014 $\pi$ Day art.

This question can be posed for different representations of π—in different bases. The distribution frequencies of 1/10, 1/100, and so on above refer to the representation of π in base 10. This is the way we're used to seeing numbers. However, if π is encoded as binary (base 2), would all the digits in 11.00100100001111... be normal? The table below shows the first several digits of π in each base from 2 to 16, as well as the natural logarithm base, $e$.

 base, $b$ $\pi_b$ base, $b$ $\pi_b$ 2 11.00100100001111 10 3.14159265358979 3 10.01021101222201 11 3.16150702865A48 4 3.02100333122220 12 3.184809493B9186 5 3.03232214303343 13 3.1AC1049052A2C7 6 3.05033005141512 14 3.1DA75CDA813752 7 3.06636514320361 15 3.21CD1DC46C2B7A 8 3.11037552421026 16 3.243F6A8885A300 $e$ 10.10100202000211 source: virtuescience.com

Because the digits in the numbers are essentially random (this is a conjecture), the essence of the art is based on randomness.

A vexing consequence of π being normal is that, because it is non-terminating, π would contain all patterns. Any word you might think of, encoded into numbers in any way, would appear infinitely many times. The entire works of Shakespeare, too. As well, all his plays in which each sentence is reversed, or has one spelling mistake, or two! In fact, you would eventually find π within π, but only if you have infinite patience.

This is why any attempts to use the digits of $\pi$ to infer meaning about anything is ridiculous. The exact opposite of what you find is also in $\pi$.

#### Stoneham's constant

A number can be normal in one base, but another. For example, Stoneham's constant,

$\alpha_{2,3} = 1/2 + 1/(2^{3^1} 3^1) + 1/(2^{3^2} 3^2) + 1/(2^{3^3} 3^3) + ... + 1/(2^{3^k} 3^k) + ...$

is 0.54188368083150298507... in base 10 and 0.100010101011100011100011100... in base 2.

Stoneham's constant is provably normal in base 2. In some other bases, such 6, Stoneham's constant is provably not normal.

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# Find and snap to colors in an image

Sat 29-12-2018

One of my color tools, the $colorsnap$ application snaps colors in an image to a set of reference colors and reports their proportion.

Below is Times Square rendered using the colors of the MTA subway lines.

Colors used by the New York MTA subway lines.

Times Square in New York City.
Times Square in New York City rendered using colors of the MTA subway lines.
Granger rainbow snapped to subway lines colors from four cities. (zoom)

# Take your medicine ... now

Wed 19-12-2018

Drugs could be more effective if taken when the genetic proteins they target are most active.

Design tip: rediscover CMYK primaries.

More of my American Scientific Graphic Science designs

Ruben et al. A database of tissue-specific rhythmically expressed human genes has potential applications in circadian medicine Science Translational Medicine 10 Issue 458, eaat8806.

# 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.