# Dominoes

> A 3D dominoes app: a many-body toppling simulation checked against the published physics of
> the domino effect, plus the standard double-six block and draw games. Runs entirely in the
> browser; no model call, no network request, no account.

https://dominoes.skillsafe.ai/

## What it does

- **Toppling.** Seven layouts — a straight line, a curve, an S-bend, a spiral, a branch that
  splits one line into two, a three-bladed fan, and a chain of tiles each half as big again as
  the last. Sliders for the number of tiles, the gap between them, tile-on-tile friction and
  tile-on-table friction. The wave speed on screen is recovered from where each tile stood and
  when it was struck, and from nothing else.
- **The game.** Double-six set, 28 tiles, two players. Block and draw variants with the
  published scoring, a stock, a boneyard floor of two tiles in the draw game, doubles laid
  crosswise, and a line of play that snakes when it runs out of table.

## The physics, in one paragraph

Each tile has two degrees of freedom: a tilt about its own leading bottom edge and a slide of
that edge along its own fall direction, held by Coulomb friction against the table. Contacts
between tiles are unilateral, solved as impulses by projected Gauss-Seidel over the whole
train at once, with two contact primitives chosen by a separating-axis rule and a second,
separate solve on pseudo-velocities for overlap recovery so that recovery can never inject
energy. The tipping threshold is exact geometry: a tile goes over when its centre of mass
passes its edge, at an angle whose tangent is the thickness over the height.

## Sources

- J. M. J. van Leeuwen, *The Domino Effect*, arXiv:physics/0401018 (2004); Am. J. Phys. 78,
  721-727 (2010). The soliton model and the table of wave speeds this engine is measured
  against.
- J. M. J. van Leeuwen, *Domino Magnification*, arXiv:1301.0615 (2013). How much bigger each
  tile in a growing chain can be.
- L. A. Whitehead, *Domino "chain reaction"*, Am. J. Phys. 51, 182 (1983). The 1.5 everybody
  quotes — a demonstration, not a limit.
- D. Ding et al., *How Fast are Domino Waves?*, arXiv:2204.07997 (2022).
- L. Dalla Pola et al., *Listen! A smartphone inquiry on the domino effect*, arXiv:2303.17231
  (2023). Measured wave speeds this app is compared with.
- "Dominoes" and "Domino toppling", English Wikipedia, for the set and the rules.

## Honesty

`/CREDITS.txt` names every source with a URL, separates what was read from what was only
cited, records a mis-cited volume number in one published bibliography, and names a record
this app could not reproduce. The page's limits section tags every number it prints and a
build-time harness re-measures each of them against the engine.

## Licence

MIT for the code and the art. The game is in the public domain.