Generator

rings-not-geometric

Where the counted pair changes along the specimen. The upper marks are the ladder's prediction from the profile alone; the lower are a blind counter walked up the built lattice. Consecutive gaps are 1.626, 1.631, 1.657, 1.763 — a spread of 8 per cent, where a single exponent would give one number repeated. On a true cone every gap would be 2.618.

Drawn at its defaults, in organs with no single exponent. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 3 essays

the blast radius of changing it

Stems and cones

An organ has no single exponent

The previous phase measured that a surface whose circumference grows as a power of arc length puts its transitions a fixed factor apart, and checked it on five surfaces. Every one of them had a single exponent, and no organ does — a fir cone is an ogive, whose exponent runs from 2 at the tip to nearly 0 at the shoulder.

Stems and cones

What one exponent reports

Fit a single shape exponent to an organ that has four of them and it returns a real quantity — the harmonic mean of what its individual steps report. Harmonic means sit below arithmetic ones, so the fit understates, systematically, in a known direction, and invisibly.

Stems and cones

How much of a cone to measure

Two rings cannot show a varying exponent — not with difficulty, but in principle, because one gap determines one exponent with nothing left to disagree. Four or five can, if each is found to within a per cent. At three per cent this specimen cannot be told from a power law however many of its rings are recorded.

All 105 generators