Multiple Pendulum

It started as a double pendulum patched in Pure Data vanilla. A double pendulum is one of the simplest physical systems that behaves chaotically: start it twice from almost the same position and after a few seconds the two runs have nothing in common. The study then grew into a chain of up to ten rods that can be added or removed while it is moving, with an example sonification in which each mass is a sine voice — pitch from its height, loudness from its speed, stereo position from its horizontal position.

The patch was conceived as a teaching tool, so it is written to be read: every section is commented. Instead of solving an N×N system of equations, each mass first moves freely under gravity for a tiny time step and each rod then pulls its two ends back to the right length — Verlet integration with distance constraints — while a once-per-frame correction measures and restores the total energy. Along the way the comments explain the Pd techniques the physics relies on: shared state through [value], [table] and [expr], the right-to-left order of [trigger], loops that run in zero time with [until], [send]/[receive] used as function calls, and ten identical voices made with [clone] and summed on a [throw~]/[catch~] bus.

I kept using the chain to drive sounds, so I turned it into a device: the same physics running inside Ableton Live, with every mass able to move a parameter on the track.

a modulator that isn’t an LFO

The motion is neither regular nor random. An LFO repeats; a random generator has no memory. A pendulum chain is continuous, has inertia, speeds up and slows down, and all its masses are connected — so whatever they control moves together in a way that feels physical. It works well on filters, sends, panning, grain positions: anything that benefits from movement that breathes instead of ticking.

mapping

A mapping column has one row per mass. For each row you choose what drives it — horizontal position, height or speed of that mass — then press Map and click any parameter on the same track, mixer included, with a Min/Max range.