Generator
necklace
A generator in the number library, called 4 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.
necklace is one function. Everything below came out of it during this
build, at parameters taken from the essays rather than invented for this page — so a figure
here is the same figure a reader meets in an essay, and if the generator changes, this page
changes with it.
At its defaults
show: "strings"
What it checks while it draws
Collected by running the family and listening to lib/verify.js, not written
here. The count is how many separate times this build put that claim to the test.
- the length is a whole number between 3 and 7 ×2
- the number of colours is a whole number between 2 and 4 ×2
- and exactly a of them are single ×1
- and the number of non-constant classes is (a^p − a)/p ×1
- every class is a single string or a full ring of p ×1
- every other class holds exactly p strings ×1
- every string of the given length is drawn ×1
- p divides a^p − a, which is what the count just showed ×1
- the classes account for every string ×1
- the classes of size one are exactly the constant strings ×1
- the figure draws every string, so there is a ceiling on how many ×1
- the length is prime ×1
- the length is prime — the whole argument needs it to be ×1
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.