This section contains various art work based on `\pi`, `\phi` and `e` that I created over the years.
Some of the numerical art reveals interesting and unexpected observations. For example, the sequence 999999 in π at digit 762 called the Feynman Point. Or that if you calculate π to 13,099,586 digits you will find love.
For some time I have been thinking about creating minimalist typographical art based on the digits of `\pi`. The `i`-ness `\pi` project was one of my first forays into this kind of art.
For each `i`th digit in `\pi`, `\pi_i`, its `i`-ness is the average of the distance between `\pi_i` and its `n` neighbouring digits.
The `i`-ness is a general property based on the neighbours of a digit. When `i` is assigned a fixed value (e.g., `i=4`) then the average distance is calculated relative to 4 instead of `\pi_i`.
Thanks to Lance Bailey for suggesting this idea.
Consider the starting sequence in `\pi = 31415...`. The 4 neighbours of the 3rd digit `\pi_3=4` are (3, 1, 1, 5). The differences between its neighbours and `\pi_3 = 4` are `-1`, `-3`, `-3` and `1`. So at this position, the average is the `i`-ness and is `-1.5` with a standard deviation of `1.7`.
If we calculate the difference relative to a fixed number (e.g. 5), we get the 5-ness of `\pi`. For the position `\pi_3` the 5-ness is the average of the differences between the neighbour digits and 5. These differences are `-2`, `-4`, `-4` and 0. The average value here is `-2.5` with a standard deviation of `1.9`.
In the `i`-ness of `\pi` poster shown above, the average is mapped onto a color and the standard deviation onto size.
Based on the color you can tell how far away from 4 the neighbours are. Brown 4s have smaller neighbours and blue/green 4s have larger ones, on average.
The type face of the main digits is Gotham. Index annotation is set in The Sans Mono Condensed Light and the neighbour and statistics annotations in Inconsolata.
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.
Drugs could be more effective if taken when the genetic proteins they target are most active.
Design tip: rediscover CMYK primaries.
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.
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%).
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.
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.
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.
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.
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.