Generator

families-are-sums

Four heads and the contact families each actually has. An arc arrives at every family that is the sum of two smaller ones; the two with no arc arriving are the generators, and on every head they are the two smallest. whorled, 144°: 2, 3, 5 — golden, 137.508°: 8, 13, 21, 34, 55, 89 — Lucas, 99.502°: 11, 18, 29, 47, 76 — rational, 137.5°: 8, 13, 21, 34, 55, 89 — 137.0°: 8, 13, 21, 29, 50, 71, 92, 113. So once a pair is counted the rest is arithmetic, and a third counted family is a prediction rather than a second measurement.

Drawn at its defaults, in why two counts are enough. It takes no options at all, so every essay calling it gets this exact drawing.

Called by 2 essays

the blast radius of changing it

The pattern itself

Every family but two is a sum

A seed head has six spiral families and everybody reports two. That looks like a convention hiding information and it is the opposite — every family but the two smallest is the sum of two others, so a third count is a prediction rather than a measurement, and a check that catches a wrong pair.

The claims, measured

What a summary throws away

Four statistics this collection has relied on turn out to be incapable of varying with the thing they describe — one is invariant to shuffling, one is fixed by a theorem, one is a parameter that stopped mattering, one is a fitted number selected into being wrong. In each case the second statistic was free and nobody had taken it.

All 114 generators