Generator

Every single-digit error in 3141592653, under weights 1…10 mod 11

A generator in the computation library, called 2 times across 1 essays. Below: what it draws with nothing chosen and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.

check-digit 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.

With nothing chosen

Every single-digit error in 3141592653, under weights 1…10 mod 11. A grid with one column per position and one row per replacement digit, marking which substitutions the check digit catches.

What each check-digit scheme catches

What each check-digit scheme catches. Bars showing, for several check-digit schemes, the fraction of single-digit errors and of adjacent transpositions the scheme detects.

What it checks while it draws

Collected by running the family and recording what it asserted, not written here. The count is how many separate times the claim was put to the test while these drawings were made.

Where it is called

Every figure on this list is drawn by the same rule, so a change to the rule changes all of them at once. That is why the list is published.

The whole library · What the figures prove