1,000,000 digits of π, φ, e and ASN.
All the artwork can be purchased from Fine Art America.
The accidental similarity number is a kind of overlap between numbers. I came up with this concept after creating typographical art about the 4ness of π.
To construct this number for π, φ and e we first write the numbers on top of each other and then identify positions for which the numbers have the same digit.
3.1415926535897932 … 21170679821 … 10270193852 … 1.6180339887498948 … 93911374847 … 08659593958 … 2.7182818284590452 … 51664274274 … 32862794349 …
These digits are then used to create the accidental similarity number. In thise case,
By definition, the decimal is held in place.
The poster shows the accidental similarity number for π, φ and e created from the first 1,000,000 digits of each number. There are 9,997 positions in which these numbers have the same digit, but only 9,996 are shown because the distance between positions is used to color the digit and I was limited by input files with 1M digits.
The distribution of distances follows a Poisson distribution with an average of 100, with about 1-1/e values being smaller than 100.
The font is Neutraface Slab Display Medium.
Any properties are accidental, but curiously ASN(π, φ, e) ≈ 1.
If you find other curiously accidental properties, let me know.
Download the first 9,997 digits of the accidental similarity number. This file provides the ASN digit index, the digit and the position from which it is sampled.
I came up with Accidental Similarity Number immediately after creating this poster of the overlap between π, φ and e.
This thought stream started with the 4ness of π.
The split plot design originated in agriculture, where applying some factors on a small scale is more difficult than others. For example, it's harder to cost-effectively irrigate a small piece of land than a large one. These differences are also present in biological experiments. For example, temperature and housing conditions are easier to vary for groups of animals than for individuals.
The split plot design is an expansion on the concept of blocking—all split plot designs include at least one randomized complete block design. The split plot design is also useful for cases where one wants to increase the sensitivity in one factor (sub-plot) more than another (whole plot).
Altman, N. & Krzywinski, M. (2015) Points of Significance: Split Plot Design Nature Methods 12:165-166.
1. Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.
2. Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking Nature Methods 11:699-700.
3. Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.
In an audience of 8 men and 8 women, chances are 50% that at least one has some degree of color blindness1. When encoding information or designing content, use colors that is color-blind safe.
As part of that collection, announced that the entire Points of Significance collection is now open access.
This is great news for educators—the column can now be freely distributed in classrooms.
I have selected several figures from our past columns and show how they evolved from their draft to published versions.
Clarity, concision and space constraints—we have only 3.4" of horizontal space— all have to be balanced for a figure to be effective.
It's nearly impossible to find case studies of scientific articles (or figures) through the editing and review process. Nobody wants to show their drafts. With this writeup I hope to add to this space and encourage others to reveal their process. Students love this. See whether you agree with my decisions!