RecreationalPhysics · companion to "The curled torus burps", plain-language edition
Turn the toy's knobs yourself. The exact numbers follow you to any setting. The measured results appear only where the simulations ran.
ExactThree arrangements of the same dots. Each rung curls one more direction, and the knob sets what curling costs.
ExactThe two cheapest ways out of a perfect tube, priced swap by swap. A missing square costs 16; a surplus square removed refunds 4λ.
ExactIn a bath, a sweep offers three route-A exits and two route-B exits on average. That count predicts the mean wait for the first exit, with nothing fitted.
MeasuredThe map: every setting of the knob from 1.05 to 1.45, at warmth 1.5, four sizes from 64 to 192 dots, thirty tubes each.
No bath. One store holds a fixed budget, and the tube can spend only that.
MeasuredThe released energy lands in stores beside the network. Few stores concentrate it; many spread it thin. Twenty tubes at each setting, λ = 1.25.
The change usually leaves a scrap: four dots of the old tube that never opened.
This page covers the paper's one change: a tube with one curled direction opening into a flat sheet, in a network with four links per dot. Three and four directions, ties between directions, and dots treated as interchangeable are outside the paper, and a separate version of the ladder covers them.
Every measured number here is from the technical paper's tables or the project's recorded result files, at the sizes and settings stated. Nothing is claimed beyond them. The clock counts sweeps of attempted swaps, not seconds. No physicist has reviewed this page.