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Physical Computing

Physical computing is how the physical world is made to run inside a computer. A waving flag, a strand of hair, smoke curling off a flame, a bridge under load — each is turned into numbers a machine can step forward in time.

FIG_002
buoyant smoke plumeincompressible advection
Fluid: a buoyant smoke plume, advected through an incompressible flow.

The core move is discretization: a continuous object becomes a finite set of points, and the laws of physics — forces, velocities, constraints — become arithmetic a machine repeats millions of times a second.

Most soft things start as a mass-spring system. Pin point masses together with springs that pull when stretched and push when squeezed, add gravity and a little damping, and a flat grid of points begins to drape, swing, and ripple like real cloth.

FIG_003
loadtensioncompression
Finite elements: a truss bridge under a rolling load, members shaded by tension and compression.

Time advances by integration. Knowing each point’s position and the forces on it, you take a small step forward — explicit Euler is simplest; Verlet and implicit schemes trade cost for stability so the simulation doesn’t blow up.

Fluids are the hard, beautiful case. The Navier–Stokes equations govern every wisp of smoke and breaking wave, and solving them on a grid or with particles is what turns code into water, fire, and moving air.

FIG_004
strand = linked segments
Hair: strands of linked segments, swaying and settling under gravity.
FIG_001
▸ cloth — 3-D verlet mass-spring sheetpinned along the topwindpoint massspring[ MASS-SPRING CLOTH ]
Cloth: a sheet discretized into point masses linked by springs, stepped forward each frame.

Stiffer matter calls for the finite element method: break a beam or a wing into small cells, solve how each one deforms under load, and stitch the answers into the stress and strain of the whole structure.

FIG_005
windliftspinning cylinder — Magnus lift
Aerodynamics: a spinning cylinder — circulation packs the flow over the top, lifting it by the Magnus effect.

Aerodynamics is physical computing aimed at air. Stream a flow past a wing, resolve the pressure above and below, and the same equations that animate smoke predict lift, drag, and whether a shape will fly.

It is where mathematics, physics, and code meet a deadline. The world won’t simplify itself, so you choose what to approximate — and a good approximation, stepped fast enough, can be indistinguishable from the real thing.

Coming soonNotes for this subject are in progress — check back later.

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A reference for the ideas behind computer science.

Written and illustrated by Amittai Siavava.

| § 2026 |