Interactive application
Interactive Video
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Computing π Through Physics

Begin with the two-block collision construction for digits of π, then change the geometry and assumptions that make it work. Phase-space views connect counts to an energy circle, while optical equivalents and deliberately biased variants reveal what is invariant and what breaks.

Collisions count an unexpected constant
CollideReflectCount
Brochure →Open project ↗
  1. π

    Count the collisions

    Start from the elastic two-block construction and its declared parameters.

  2. ◯

    Reveal phase space

    Read the same trajectory through energy geometry and unfolding.

  3. ↔

    Change the representation

    Compare mechanical and optical versions of the underlying construction.

  4. Δ

    Break an assumption

    Change restitution or support geometry and inspect the resulting bias.

The experiment explains why a counter works—and makes its failure modes just as visible.

Wedge unfolding and the corresponding radius-versus-velocity-angle portrait.
Wedge unfolding and the corresponding radius-versus-velocity-angle portrait.
Three-body collision geometry: the chamber and an energy-sphere trajectory provide complementary views.
Three-body collision geometry: the chamber and an energy-sphere trajectory provide complementary views.
The magnetic variant compares several collision setups and their rescaled-momentum portraits.
The magnetic variant compares several collision setups and their rescaled-momentum portraits.
A resistor lattice pairs the network geometry with its potential field.
A resistor lattice pairs the network geometry with its potential field.