Science lab / statistical motion

Brownian motion, one collision at a time.

Track a massive probe through a crowd of moving marbles, then change its size, density, launch direction, and surroundings to see how its path responds.

Model notes

A small mechanical model of random-looking motion

This laboratory uses a two-dimensional hard-disc model inspired by Brownian motion. Each marble has a radius and density, giving it a mass of m = ρπr2. Larger or denser marbles therefore carry more inertia than smaller or lighter ones.

Every collision is treated as elastic: momentum is exchanged along the line joining the two centres while tangential motion is retained. The repeated impacts make a tracked probe follow an irregular path even though every individual collision obeys a deterministic rule.

From a botanical puzzle to evidence for atoms

In 1827, botanist Robert Brown watched tiny particles released from pollen grains wander continually in water. He repeated the observation with non-living materials, helping to rule out a specifically biological cause. The phenomenon later took his name.

Albert Einstein's 1905 treatment connected this visible wandering to countless unseen molecular impacts and predicted measurable diffusion. Jean Perrin's painstaking experiments tested those predictions and helped make the molecular reality of matter experimentally persuasive; that work was recognised by the 1926 Nobel Prize in Physics.

Where similar motion appears

Brownian motion can be observed in sufficiently small pollen or mineral particles in water, pigment particles in colloidal suspensions, and fine smoke or dust suspended in still air. Thermal jostling also contributes to microscopic motion inside cells, though real cells add flows, binding, and active molecular transport that this model omits.

What this model leaves out

This is an idealised teaching model, not a complete molecular-dynamics simulation of a real fluid. It is two-dimensional, uses perfectly hard circular particles, and omits molecular forces, viscosity, rotation, and three-dimensional effects.

Things to try

  • Raise the background temperature and watch the probe path become more agitated.
  • Increase probe density while keeping its radius fixed to give collisions less influence.
  • Make the probe larger so it receives impacts from more neighbours.
  • Compare the canvas trail with the full-space trajectory and speed history.

Sources and further reading

Deep instrument

Hard-disc collision workbench

Configure the bath and probe, then compare its live trail with its trajectory in position space.

Simulation running

Particle bath
Probe particle

Under the hood

The mathematics used in this simulation

Each particle is a circular hard disc. Its mass is its density multiplied by its two-dimensional area. Positions advance with a fixed 1/120-second physics step; rendering can happen at a different rate without changing the collision calculation.

Mass and motion

m = ρπr2

xt+Δt = xt + vΔt

A wall collision reverses only the velocity component perpendicular to that wall.

Elastic collision impulse

j = −(1 + e) (vb − va) · n / (1/ma + 1/mb)

Here n points between the particle centres and e = 1 for a perfectly elastic collision. The equal and opposite impulse changes both velocities, conserving total momentum and kinetic energy apart from floating-point error.

Keeping contacts stable

Any small overlap is removed in inverse proportion to mass, so the lighter disc moves farther. A spatial grid checks only particles in the same or neighbouring cells instead of comparing every possible pair.