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.
Outliers can degrade the fit of linear regression models when the estimation is performed using the ordinary least squares. The impact of outliers can be mitigated with methods that provide robust inference and greater reliability in the presence of anomalous values.
We discuss MM-estimation and show how it can be used to keep your fitting sane and reliable.
Greco, L., Luta, G., Krzywinski, M. & Altman, N. (2019) Points of significance: Analyzing outliers: Robust methods to the rescue. Nature Methods 16:275–276.
Altman, N. & Krzywinski, M. (2016) Points of significance: Analyzing outliers: Influential or nuisance. Nature Methods 13:281–282.
Two-level factorial experiments, in which all combinations of multiple factor levels are used, efficiently estimate factor effects and detect interactions—desirable statistical qualities that can provide deep insight into a system.
They offer two benefits over the widely used one-factor-at-a-time (OFAT) experiments: efficiency and ability to detect interactions.
Since the number of factor combinations can quickly increase, one approach is to model only some of the factorial effects using empirically-validated assumptions of effect sparsity and effect hierarchy. Effect sparsity tells us that in factorial experiments most of the factorial terms are likely to be unimportant. Effect hierarchy tells us that low-order terms (e.g. main effects) tend to be larger than higher-order terms (e.g. two-factor or three-factor interactions).
Smucker, B., Krzywinski, M. & Altman, N. (2019) Points of significance: Two-level factorial experiments Nature Methods 16:211–212.
Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments.. Nature Methods 11:597–598.
Celebrate `\pi` Day (March 14th) and set out on an exploration explore accents unknown (to you)!
This year is purely typographical, with something for everyone. Hundreds of digits and hundreds of languages.
A special kids' edition merges math with color and fat fonts.
One moment you're
:) and the next you're
Make sense of it all with my Tree of Emotional life—a hierarchical account of how we feel.
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.