Interactive simulations have a unique power: they let you manipulate variables and see consequences instantly, building the kind of physical intuition that only comes from experiment. The following ten simulations cover different branches of physics and mathematics, from undergraduate topics to concepts that don't appear in standard curricula but should. Each is available directly in your browser โ no installation required.
The List
Double Pendulum โ Chaos and Sensitive Dependence
Launch two pendulums from nearly identical starting positions and watch them diverge within seconds. The definitive demonstration of sensitivity to initial conditions. Perfect for introducing chaos theory without equations โ the behaviour is immediately visible and viscerally surprising.
SPH Fluid Simulation โ Continuum Mechanics in Particles
Drag your cursor through a fluid and watch pressure waves propagate. This Smoothed Particle Hydrodynamics simulation demonstrates the Navier-Stokes equations in action โ density, pressure, and viscosity all visible as particle behaviour. Invaluable for computational physics modules.
Lorenz Attractor โ Strange Attractors and Fractal Geometry
Watch the butterfly-shaped Lorenz attractor trace its never-repeating path through three-dimensional state space. Adjust the system parameters and observe transitions between chaos, periodic orbits, and fixed points. Essential for any course on dynamical systems or non-linear physics.
Cellular Automata โ Emergence from Simple Rules
Conway's Game of Life and its variants show how extraordinarily complex, life-like patterns emerge from four simple rules applied to a grid of cells. A profound demonstration of emergence โ the whole being more than the sum of its parts โ accessible to anyone from GCSE upward.
Boids โ Collective Behaviour and Emergence
Three simple rules โ separation, alignment, cohesion โ produce realistic flocking, murmurating, and schooling behaviour. A beautiful demonstration of how collective intelligence emerges from local interactions, with direct applications to statistical mechanics and self-organisation.
Disease Spread โ SIR Model and Epidemiology
Watch an infection propagate through a population. Adjust transmission rate, recovery time, and vaccination fraction and observe how the epidemic curve changes. Directly connects to the SIR differential equations taught in mathematical biology and provides tangible intuition for Rโ and herd immunity thresholds.
Sorting Algorithms โ Complexity Made Visual
Watch quicksort, mergesort, bubble sort, and heapsort race side by side on arrays of different sizes. The visual difference between O(n log n) and O(nยฒ) algorithms is immediately apparent. Essential for anyone taking computational physics, numerical methods, or computer science alongside their physics degree.
Mandelbrot Set โ Complex Dynamics and Fractal Boundaries
Zoom into the Mandelbrot set's infinitely complex boundary โ a fractal generated by iterating the simplest possible quadratic map in the complex plane. Connects directly to complex analysis, Julia sets, and the theory of iterated function systems. The visual complexity arising from z โ zยฒ + c is genuinely astonishing.
Quantum Double Slit โ Wave-Particle Duality
Watch the interference pattern build up one particle at a time. The double-slit experiment is quantum mechanics' most famous demonstration โ a particle passes through both slits simultaneously, interferes with itself, and lands in a predictable probability distribution. Interactive control over slit separation and particle energy.
N-Body Gravity โ From Newton to Galaxy Formation
Simulate thousands of gravitating bodies using Barnes-Hut O(N log N) acceleration. Watch galaxy discs form, stars slingshot around massive objects, and binary systems evolve. Directly relevant to computational astrophysics modules and a compelling demonstration of how complex structure emerges from simple gravitational attraction.
How to Use These in Your Studies
The most effective way to use interactive simulations is not passive observation but active experiment. Before starting, form a prediction: what will happen if you increase this parameter? Then run the simulation and check. When your prediction is wrong โ and it often will be โ ask why. That moment of surprise is where learning happens.
For exam preparation, use simulations to build intuition about limiting cases. What happens to the double pendulum as the amplitude decreases toward zero? (It becomes a simple pendulum โ predictable.) What happens to the Lorenz attractor as ฯ decreases below 1? (The fixed point at the origin becomes stable and the chaos disappears.) These are the kinds of questions that separate students who understand the physics from those who can only reproduce derivations.
For research projects and extended investigations, every simulation on this site can be used as a starting point for data collection. Measure the divergence time of the double pendulum as a function of initial angle difference and fit it to the expected exponential form. Measure how the N-body simulation's energy conservation depends on timestep size. These are genuine physics investigations with publishable-quality methodology.