Generator

collatz

A generator in the dynamics library, called 0 times across 0 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.

collatz 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

The Collatz orbit of 27Halve an even number, triple an odd one and add one; the sequence plotted on a logarithmic scale.9232127 reaches 1 in 111 steps, after climbing to 9232the vertical scale is logarithmic, because the climb is the interesting part and it is steep

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 whole library · What the figures prove