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 invented the 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.
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