Generator

fourier

A generator in the analysis library, called 7 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.

fourier 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

A square wave from 5 sine wavesThe sum of the first 5 harmonics, compared with the square wave it approaches.−π−π/2π/2π-115 terms

show: "progression"

Partial sums of the square waveApproximations using 1, 3, 7, 21 terms; the corners sharpen but a fixed overshoot remains.-111 term-113 terms-117 terms-1121 terms

show: "gibbs"

The overshoot that never goes awayZoomed in on the jump: adding terms narrows the overshoot but does not shrink its height.-0.200.20.40.60.810.911.11.27 terms21 terms61 terms≈ 9% over, always

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.

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.

The whole library · What the figures prove