Devlog #14 — When a Simulation Becomes a Thinking Tool

Illustration vs. Discovery

There's a spectrum for scientific visualisations. At one end: a diagram you already know the answer to, rendered in pretty colours. At the other: an interactive model where the outcome surprises even the builder. Most educational simulations sit closer to the first. We've been trying to push ours toward the second.

The tell-tale signs of a thinking tool vs. a decoration:

You can ask it a question it wasn't explicitly designed to answer
Changing a parameter produces something you didn't predict
You catch yourself saying "wait — why does that happen?"
You use it to resolve a disagreement, not just confirm existing understanding

Moments Where Our Simulations Taught Us Something

Ballistics Simulator

The optimal angle isn't 45° in air

We built the ballistics sim to show the classic parabolic trajectory. Then someone from Twitter asked: "Does wind resistance change the optimal launch angle?" We didn't know. We set constant drag and swept launch angle from 30° to 60°. The range curve peaked at around 40° — not 45°. At higher muzzle velocities, it shifted even lower. We ended up chasing this down through the underlying ODEs. It's correct, and it's not obvious from the textbook derivation that ignores drag.

→ The sim told us what to look for. The maths confirmed it. Not the other way around.

Double Pendulum

Chaos onset depends on initial angle, not just energy

We expected the double pendulum to become chaotic above a certain initial angle. It does. But watching 100 simultaneous pendulums with randomly perturbed starting positions, we discovered that the onset of chaotic divergence was highly uneven — some starting configurations stayed coherent far longer than others at the same total energy. This led us to read about the Lyapunov exponent landscape, which we'd never have done without staring at 100 diverging paths.

→ Visualising the ensemble, not just the trajectory, was the key.

Disease Spread (SIR Model)

Superspreaders create a different curve shape, not just a taller one

We added agent heterogeneity to our SIR model — some agents had higher contact rates (superspreaders). We expected the epidemic peak to just be higher and earlier. Instead, the curve shape changed: a sharp fast-rising initial peak followed by a slower secondary wave as the superspreaders burned through the susceptible population, then the disease smouldered through the less-connected population. This matched real COVID-19 wave patterns we weren't originally trying to model.

→ The simulation reproduced an observed real-world pattern before we understood why.

Bridge Designer

Triangulation matters more than thickness

We built the bridge sim to show structural stress distribution. A user asked: "Is it better to add a thicker top chord or add more diagonals?" We tested both. Adding diagonals improved load capacity by 3× more than doubling chord thickness, for the same material cost. This is known to civil engineers — but neither of us had made it visceral until we watched the non-triangulated bridge collapse under the same load that the triangulated version handled easily.

→ "I know this in principle" and "I understand this" are different states of knowledge.

What Makes the Difference

Looking back at these moments, they share some properties. The simulation needed to:

Be numerically honest — wrong integrators or artificial stabilisation hides the real behaviour
Allow sweeping parameters — a single fixed simulation is a demonstration; a slider is a question-answering device
Show enough detail — individual agents, not just aggregate statistics; trajectories, not just endpoints
Run fast enough to explore — if you have to wait 30 seconds per run, you don't iterate; you don't discover

"To understand something deeply, it helps to be able to change it and watch what breaks."

This is our design goal for the next generation of simulations: not just physically accurate animations, but genuinely interactive models where students can form hypotheses, run experiments, and arrive at understanding through their own exploration. Not textbook. Laboratory.