Domino Run Simulator

How the Domino Run Simulator works

A domino run is one of the cleanest demonstrations of stored energy there is. A standing domino has its centre of mass raised above the floor. Tipping it past its balance point lets gravity turn that height into motion, and the falling domino hands some of that motion to the next one. As long as each tile delivers more than its neighbour needs to tip, the wave keeps going on its own. This simulator runs that as real rigid-body physics with the open-source Matter.js engine. Each domino has mass, floor friction and a pivot about its bottom edge, and the wave you see comes out of the collisions rather than a scripted animation.

How the domino run simulator works

Press and drag along the floor to lay a straight line, or click to place tiles one at a time. A fresh row is laid across the floor when the page loads, so you can press Topple straight away. Topple gives the first upright domino a sideways push near its top, like a flick of a finger, and starts the clock. Stand them up returns every tile to upright where it lies, so you can rerun the same layout after changing a slider. Clear empties the floor. The sliders apply to tiles already placed as well as new ones.

The two controls are the ones that matter in a real run:

• Domino height, from 20 to 100 pixels. Tile thickness is a fifth of the height, close to the proportions of a standard 48 mm by 24 mm by 7.5 mm toppling domino stood on end.
• Spacing, set as a multiple of the height, from 0.3 to 1.2. It is measured between tile centres, so the same setting gives the same behaviour at any size.

Why spacing decides everything

A falling domino has to hit its neighbour above that tile's centre of mass, or it only shoves the base along the floor. It also needs time to pick up speed before contact.

Professional domino builders work in the same range. Most lay standard tiles about half to two thirds of a tile height apart, because that leaves room for a finger if a tile goes early and still gives a reliable strike.

Where the physics shows up

• Wave speed grows with height. In a real row, the wave speed is roughly proportional to the square root of the domino height, so tiles four times taller carry the wave about twice as fast. For example, lay a full row at height 30, topple it and note the run time, then press Stand them up, set the height to 90 and run it again.
• Dominoes amplify. Because each tile only needs a nudge to tip, a domino can knock over one about one and a half times its own size. The physicist Lorne Whitehead showed in 1983 that a chain of steadily growing dominoes turns a tiny push into a very large fall, and it is a standard classroom demonstration of energy release.
• Records run into millions. The Domino Day events in the Netherlands toppled more than 4 million tiles in a single chain in 2009. Runs that size are built in sections with gaps that are closed only at the end, since one early fall could otherwise wipe out weeks of work.

Reading the result

The panel updates about four times a second:

• Dominoes is the number of tiles on the floor.
• Fallen counts tiles tilted more than about 29 degrees from upright, with the share of the row in brackets. 100 % means the whole run went.
• Still standing is the rest. If the number freezes above zero while nothing moves, the wave died at a gap or a tile that was too far away.
• Run time is the seconds since you pressed Topple. Divide the length of the row by it for the wave speed, or compare two runs of the same length at different settings.

Tips and pitfalls

• Build in short lines. Several short drags give you control over the gaps; one long drag can leave a tile too close to a wall or its neighbour.
• Mixed heights. Change the height slider between lines to build a growing chain. A short domino striking a much taller one low down will often fail, just as in real life.
• Clicks add, never replace. Clicking on top of an existing tile places a second one in the same spot, which jams the run. Clear and relay a messy section rather than patching it.
• Compare with 3D. The 3D domino toppling tool runs the same idea with depth and curves, and the marble run and Newton's cradle simulators show other ways energy passes along a chain.

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