Pursuit of Equilibrium logoPursuit of Equilibrium

Chapter 2

PENDULUMS

A PHYSICS-BASED GENERATIVE ART COLLECTION

by BEN STRAUSS

Motion Carries Structure

Pendulums is a physics-driven generative art system modeled after a Blackburn pendulum. Each artwork emerges from a unique configuration of forces including period ratios, amplitudes, damping, and phase offsets.

Once initialized, the system runs deterministically. The motion unfolds stroke by stroke, revealing patterns that are not drawn by hand but discovered through the behavior of the system itself.

The collection contains 512 outputs from this system, each representing a different physical configuration.

The System

This is the engine behind every piece in the collection. Each time you click Generate, a new system comes to life, just like it will during the actual mint. Click the artwork to watch the pendulum draw itself, stroke by stroke, in real time. You'll also find each generated artwork's output profile: a snapshot of the variables that shaped its motion, from period ratios and amplitudes to damping, line type, and runtime.

About Pendulums

MOTION AS MEMORY

Motion is not just movement. It is memory and math. It is the quiet negotiation between chaos and order, friction and flow.

Chapter II of Pursuit of Equilibrium did not begin as art, it began as a tool. I needed a way to preview pendulum motion, to plan exposures, fine-tune ratios, and avoid hours in the dark chasing perfection. But the more I built, the more the system started to feel like a collaborator. It was not just solving problems anymore. It was making choices. Expressing something.

FROM LIGHT TO CODE

Chapter I, Lux, was entirely physical. Real pendulums swung in silence. Long exposures etched their paths onto sensors, capturing motion that would otherwise remain invisible.

But precision required dozens of failed attempts. Swing ratios had to be dialed in manually. A few millimeters of slack could destroy symmetry. The work was meditative, but exhausting.

So I built a simulator. Just to preview motion. Nothing more. Then the code started surprising me.

A real-world pendulum exposure beside an early simulation preview
A real-world pendulum exposure, Lux No. 6 (left) vs. an early simulation preview (right) used to plan swing ratios.

THE BLACKBURN PENDULUM

Most pendulums swing along one axis. A Blackburn pendulum swings in two, with one axis swinging at a faster rate than the other. When released together, they produce interferance patterns that fold into elegant designs known as Lissajous figures.

No motors. No effects. Just the raw outcome of natural ratios. It is a system that creates complexity from simplicity and rhythm from physics. What you see in this collection is that same system, modeled, coded, and reborn.

Historic harmonograph Lissajous pattern beside an algorithmic output
An early Lissajous pattern produced via a harmonograph by S.C. Tisley, circa late 1800s (left), alongside a simplified, similar output generated by my algorithm (right). The pattern above is from a 3:4 period ratio.

A SYSTEM WITH IMPERFECTIONS

This is not a clean or idealized simulation. It is a digital twin of the real thing, with damping, friction, asymmetry, and entropy. Each drawing is a fossilized memory of a system in motion, shaped by variables like period, amplitude, phase offset, and decay. Some systems swing cleanly. Others drift or collapse.

That tension, between precision and collapse, is where the beauty lives. The code does not simulate reality. It mirrors it.

Algorithm controls for pendulum system parameters
Screen shots from the algorithm, showing tunable physical parameters like damping, amplitude, period offset, period lengths, and phase offsets, all of which shape the final aesthetic of the output.

THE PERFECTION SCORE

Not all systems are equal. Some yield minimal, balanced loops. Others spiral into dense and expressive tangles.

To make the structure of the system visible, I created a rating method. Every piece starts with a score of 100. Deductions are applied for imperfections like asymmetry, imbalance, short runtimes, and high period offsets. Bonus points are awarded for elegant ratios with low least common multiples.

The result is a Perfection Score, and a System Rating from Emergent to Perfect. It does not dictate taste. It reveals the path the system took.

Emergent: below 60
Forming: 60-69
Proficient: 70-79
Notable: 80-84
Advanced: 85-89
Superior: 90-94
Perfect: 95+

Click the buttons below to see example outputs for each category:

Emergent system example 1
Emergent system example 2
Emergent system example 3
Emergent system example 4

Example outputs for each of the 7 system perfection categories.

AN ACT THAT PERFORMS

These are not just static images. Each piece animates itself in real time. When activated, the algorithm draws the artwork stroke by stroke using its own pendulum logic.

Some systems draw in under 30 seconds. Others take over 30 minutes. Once complete, the image erases itself and begins again. This loop continues indefinitely.

This is not a replay. It is the original system performing its own creation. What you are watching is motion encoded in code and expressed over time.

Time progression snapshots of an animated pendulum output
Snapshots from the progression of a pendulum output in animated mode, showing the drawing as it unfolds in real time.

FROM THE UNIVERSE TO THE CANVAS

This project is not about randomness. It is not aesthetic trickery. It is the re-creation of physical law in code, rendered with just enough imperfection to make it human. The code does not pretend to be a pendulum. It is one.

Behind each image is a simulation unfolding in time. In animated mode, you are not watching a replay, you are watching the algorithm perform the drawing, governed by its own rules. The result is not a representation. It is a trace of motion. A system coming to rest.

This is Chapter II. The universe is the algorithm. The code is the pendulum. And you are the witness.