Interactive physics
A mass on a fixed arm governed by gravity. At small angles it approximates simple harmonic motion. As the angle increases, nonlinearity stretches the period — the swing grows slower and asymmetric.
Two linked arms, each with its own mass. A canonical example of deterministic chaos: the equations are exact, yet above ~60° the motion becomes practically unpredictable. Infinitesimally different starting conditions diverge exponentially.
The physics
The single pendulum is complicated. It has one moving part, governed by one rule: gravity pulls the bob back toward centre. Given the starting angle, you can predict exactly where it will be at any point in the future. It is analysable, controllable, and fully knowable. Engineers love it.
The double pendulum is complex. A second arm is attached to the end of the first. The rules are still exact — nothing random is happening — but the two arms interact with each other in ways that make the overall behaviour impossible to predict beyond a short time horizon. Start it twice from nearly identical positions and the paths will diverge completely within seconds. This is called deterministic chaos: governed by laws, but not by forecasts.
Turn on Trails and increase the starting angle above 90°. The single pendulum draws the same clean arc, over and over. The double pendulum fills the canvas with a pattern that never repeats. Same simulation engine. Same physical laws. Fundamentally different kind of system.
Most of our planning tools — logframes, theories of change, causal models — are built for complicated systems. They assume that if you understand the parts, you can predict the whole. The double pendulum is a reminder that this assumption breaks down as soon as components interact in non-trivial ways. Social systems, organisations, and communities in transition behave much more like the double pendulum than the single one.
In a complex system, small differences in starting conditions compound over time. This is not a flaw or a gap in knowledge — it is a structural property of the system. It means that two communities receiving identical interventions can produce very different outcomes, not because one "worked" and one didn't, but because the systems they were embedded in were not identical — and never could be.
About this resource
This simulation is part of a series of interactive teaching resources produced by the School of Systems and Complexity (SSC) — a practitioner school working at the intersection of systems thinking, complexity science, and organisational change. SSC develops education, advisory practice, and community of practice programmes for those navigating environments where the complicated and the complex meet.
If you are a practitioner, educator, researcher, or leader working with systems that resist straightforward analysis — this is the work we do.
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