Physics Topic Tree
Explore interactive physics simulations and theoretical articles structured by physical domain. Use the controls below to filter nodes by type.
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Classical Mechanics & Kinematics
Motion, forces, oscillating systems, dynamics, and gravitational orbits.
Harmonic Oscillator
Interactive phase-space exploration of a driven, damped harmonic oscillator.
Double Pendulum
Interactive Lagrangian simulation of the double pendulum. Drag the bobs, tune the parameters, watch chaos unfold.
Spring Pendulum
Interactive Lagrangian simulation of the spring pendulum (elastic pendulum). Drag the bob, tune the parameters, watch energy exchange.
Pendulum Wave
N simple pendulums tuned so they complete successive integer numbers of oscillations in a fixed period. The result is a travelling wave that undergoes constant metamorphosis.
Buoyancy & Stability
Interactive 2D rigid body simulation exploring Archimedes
Spirograph
Interactive Spirograph generator. Simulate hypotrochoids and epitrochoids by rolling one circle inside or outside another.
Harmonograph
Interactive harmonograph simulation. Explore complex Lissajous curves drawn by coupled damped pendulums.
Lissajous Figures
An interactive exploration of Lissajous figures and complex harmonic motion.
Harmonic Oscillator
An introduction to the simple harmonic oscillator, the fundamental model of physics.
The Spring Pendulum: An Elastic Dance
An introduction to nonlinear dynamics and energy exchange through the lens of the spring pendulum (elastic pendulum).
Pendulum Wave: The Dance of Time
An introduction to the pendulum wave experiment, explaining how simple harmonic motion and careful timing create mesmerizing, dancing patterns.
Buoyancy & Stability
An introduction to Archimedes
Spirograph: The Mathematics of Rolling Circles
An introduction to the Spirograph, explaining how rolling circles create complex hypotrochoids and epitrochoids.
Harmonograph: Drawing with Pendulums
An introduction to the harmonograph, explaining for high schoolers how coupled damped pendulums trace complex Lissajous curves based on musical ratios.
Lissajous Figures
An introduction to Lissajous figures, complex harmonic motion, and parametric equations.
Kepler's Laws of Planetary Motion
An introduction to Kepler
Fluid Dynamics & Transport
Continuum mechanics, Navier-Stokes flow, diffusion, and Brownian particle trajectories.
Fluid Dynamics
Real-time 2D Navier-Stokes fluid simulation. Paint dye, inject vortices, and watch the Kelvin-Helmholtz instability roll up right in front of you.
Brownian Motion
Interactive Brownian motion simulation. Watch a large pollen particle get buffeted by the random thermal motion of smaller fluid molecules.
Fluid Dynamics: The Mathematics of Flow
An introduction to fluid dynamics, the Navier-Stokes equations, and the Kelvin-Helmholtz instability for high school students.
Fluid Mechanics
An introduction to fluid mechanics and Navier-Stokes equations.
Brownian Motion: The Mathematics of the Random Walk
An advanced exploration of Brownian motion, the Langevin equation, and the Einstein relation linking diffusion to thermal energy.
Thermodynamics & Statistical Mechanics
Kinetic theory, entropy, phase transitions, and lattice spin dynamics.
Hard Disk Gas
2D molecular dynamics of elastic hard disks. Watch Maxwell-Boltzmann emerge from Newtonian mechanics.
Ising Model
Interactive 2D Ising model. Metropolis Monte Carlo on a 200×200 square lattice — watch ferromagnetic domains form, coarsen, and fractalise at the Onsager critical temperature.
Hard Disk Gas: Understanding Molecular Dynamics
An introduction to statistical mechanics and the Maxwell-Boltzmann distribution through the lens of a simple 2D hard disk gas.
Ising Model: Statistical Mechanics
An introduction to the Ising Model, a mathematical model of ferromagnetism in statistical mechanics, explaining spontaneous magnetization and phase transitions.
The Laws of Thermodynamics
An introduction to the Laws of Thermodynamics, entropy, and energy conservation.
Entropy and the Arrow of Time
An introduction to entropy, the second law of thermodynamics, and the arrow of time.
Waves, Acoustics & Optics
Wave interference, frequency analysis, Doppler shift, and resonance patterns.
Doppler Effect
Interactive simulation of the Doppler Effect. Watch wavefronts compress and expand as a source moves.
Wave Interference
Classical wave superposition from multiple point sources. Drag sources to reshape fringes; switch between in-phase and anti-phase configurations.
Chladni Figures
Sand on a vibrating plate forms Chladni figures — the nodal-line eigenmodes of the 2D wave equation. 2 000 simulated grains driven by the time-averaged displacement gradient settle onto whichever mode (m, n) you choose.
Fourier Drawing Machine
Any closed curve, decomposed into a chain of rotating epicycles via the discrete Fourier transform.
The Doppler Effect
An exploration of the Doppler Effect, deriving the frequency shifts for moving sources and observers, and analyzing the geometry of Mach cones.
Wave Interference: When Waves Collide
An introduction to classical wave superposition, wave interference, and the geometry of fringes.
Chladni Figures: Seeing Sound
An introduction to Chladni figures, explaining how sound waves and vibrations create beautiful geometric patterns on metal plates, explained for high schoolers.
Fourier Series: Drawing with Circles
An introduction to the Fourier Transform and how complex curves can be decomposed into a chain of rotating epicycles.
Electromagnetism & Field Theory
Vector fields, electrostatics, Coulomb potentials, and field line visualisations.
Quantum Mechanics & Atomic Physics
Wave-particle duality, photon scattering, tunneling, entanglement, and wave packet dispersion.
Photoelectric Effect
Interactive simulation of the Photoelectric Effect. Watch photons strike a metal surface and eject electrons.
Rutherford Scattering
A simulation of alpha particles scattering off a heavy nucleus. Observe classical Coulomb trajectories and cross-sections.
Quantum Double
A Gaussian wave packet diffracting through two slits in 2D. Split-operator FFT integration of the time-dependent Schrödinger equation, showing quantum interference directly.
Wave Packet
A Gaussian wave packet propagating under the time-dependent Schrödinger equation. Crank-Nicolson integration with adjustable potentials.
The Photoelectric Effect
An introduction to the photoelectric effect, photons, and wave-particle duality.
Rutherford Scattering
An introduction to Rutherford scattering, the plum pudding model, and the discovery of the atomic nucleus.
Quantum Double-Slit: The Mystery of Matter Waves
An introduction to the quantum double-slit experiment, matter waves, and quantum interference.
Wave Packet: Quantum Dynamics
An introduction to the quantum wave packet and the time-dependent Schrödinger equation, explained for high schoolers.
Quantum Tunneling
An introduction to quantum tunneling, wave-particle duality, and how particles pass through barriers.
Quantum Entanglement
An introduction to quantum entanglement, spooky action at a distance, and Bell
Schrödinger's Cat
An introduction to Schrödinger
Astrophysics, Relativity & Cosmology
Spacetime curvature, relativistic geodesics, N-body gravitation, and Hawking radiation.
N
Real-time N-body gravitational simulation. Explore the figure-8 choreography, binary stars, and stellar clusters with symplectic integration.
Special Relativity
Interactive Minkowski spacetime diagrams with live Lorentz boosts. Drag the velocity slider to change reference frames and watch simultaneity break, time dilate, and lengths contract.
Black Hole Geodesics
Photon and particle paths in Schwarzschild spacetime. Light bending, the photon sphere, orbital precession, ISCO — all integrated in your browser from the geodesic equations.
N-Body Gravity: The Cosmic Dance
An introduction to gravitational fields, Newton
Special Relativity
An introduction to Special Relativity, Minkowski diagrams, Lorentz boosts, and the twin paradox.
Black Hole Geodesics: Navigating Curved Spacetime
An introduction to general relativity, curved spacetime, and black hole geodesics for high school students.
Hawking Radiation
An exploration of Hawking radiation, quantum field theory in curved spacetime, and black hole thermodynamics.
Chaos, Fractals & Non-Linear Dynamics
Strange attractors, bifurcation trees, non-linear solitons, iterative fractals, and chaotic magnetic pendulums.
Bifurcation & Chaos
The logistic map
Lorenz Attractor
Interactive integration of the Lorenz system. Tune σ, ρ, β and watch deterministic chaos unfold.
Magnetic Pendulum
A damped pendulum above three magnets traces fractal basins of attraction. Click the map to watch a live trajectory settle.
Standard Map
The Chirikov–Taylor standard map: an area-preserving twist of phase space that mixes regular KAM tori with stochastic chaos. Tune K, watch the last torus break at Greene
Mandelbrot Set
Interactive explorer of the Mandelbrot set. Zoom into the boundary between order and chaos, watch the escape-time algorithm carve infinite self-similar detail.
Julia Set Explorer
Explore the Julia sets of z → z²+c. Click the Mandelbrot navigator to select c and watch the Julia set switch between connected fractal and Cantor dust in real time.
Barnsley Fern
Interactive explorer of the Barnsley Fern. An iterated function system (IFS) that creates a mathematically accurate model of a fern.
Chaos Game
Interactive explorer of the Chaos Game. An iterative method of generating fractals, like the Sierpinski triangle, using a simple geometric rule.
KdV Solitons
Pseudospectral integration of the Korteweg–de Vries equation. Watch solitons pass through each other without deformation — particle-like waves that survive every collision.
Bifurcation & Chaos: The Path to Unpredictability
An introduction to deterministic chaos, the logistic map, and the period-doubling route to chaos.
The Butterfly Effect: Understanding the Lorenz Attractor
An introduction to deterministic chaos, the butterfly effect, and the Lorenz Attractor, explained for high school students.
Magnetic Pendulum
An introduction to the magnetic pendulum experiment, explaining chaos theory and fractals.
The Standard Map
An introduction to the Standard Map and Hamiltonian chaos, explained for high schoolers.
The Mandelbrot Set: The Boundary of Chaos
An introduction to the Mandelbrot Set, complex dynamics, and fractals, explained for high schoolers.
Julia Sets: The Mandelbrot Set's Cousins
An introduction to Julia Sets, complex dynamics, and fractals.
Barnsley Fern: Nature's Math
An introduction to the Barnsley Fern, explaining how a simple Iterated Function System generates a mathematically accurate model of a fern.
The Chaos Game: Order from Randomness
An introduction to the Chaos Game, explaining how a simple geometric rule involving randomness generates perfect fractal structures like the Sierpinski Triangle, tailored for high-schoolers.
KdV Solitons: Waves That Act Like Particles
An introduction to the Korteweg-de Vries equation and solitons, particle-like waves that survive collisions.
The Double Pendulum: A Study in Chaos
An introduction to deterministic chaos and Lagrangian mechanics through the lens of the double pendulum.
Complex Systems, Automata & Pattern Formation
Self-organization, cellular automata, epidemic modeling, reaction-diffusion, and emergence.
Game of Life
Conway
Cellular Automata
Wolfram
Langton's Ant
Langton
Boids Flocking
Craig Reynolds
Kuramoto Oscillators
Coupled phase oscillators and the emergence of spontaneous synchronisation. Watch incoherence collapse into a locked rotating cluster as coupling crosses the critical threshold.
BTW Sandpile
The Bak–Tang–Wiesenfeld sandpile: drop grains on a 192×192 lattice, watch avalanches cascade, and see the power-law avalanche-size distribution emerge live. The cleanest example of self-organised criticality.
Percolation
Interactive exploration of percolation and the emergence of spanning clusters.
Diffusion
Brownian walkers freeze on contact with a growing cluster, producing fractal crystals that mirror lightning, coral, and snowflake arms.
L
Interactive explorer of Lindenmayer Systems (L-Systems). Generate fractal plants, Koch curves, and dragon curves using simple string replacement rules.
SIR Epidemic Model
Interactive exploration of the SIR (Susceptible, Infectious, Recovered) epidemic model.
Lotka
Interactive phase-space and time-series exploration of the Lotka-Volterra predator-prey equations.
Reaction
Gray-Scott reaction-diffusion system producing Turing patterns — spots, worms, coral, and self-replicating structures from two coupled PDEs.
Cloth Simulation
Interactive cloth simulation using Verlet integration and structural constraints.
Buffon's Needle
A Monte Carlo simulation of Buffon
Galton Board
Interactive simulation of a Galton Board demonstrating the Central Limit Theorem and the emergence of the binomial distribution.
Conway's Game of Life: Emergence and Complexity
An introduction to Conway
Cellular Automata: Computation from Simplicity
An introduction to Wolfram
Langton's Ant: Chaos to Order
An introduction to Langton
Emergence: Unpacking the Boids Algorithm
An in-depth exploration of Craig Reynolds
Kuramoto Oscillators: Spontaneous Synchronization
An introduction to coupled phase oscillators and spontaneous synchronization through the Kuramoto model.
Self-Organised Criticality: The Bak–Tang–Wiesenfeld Sandpile
An introduction to self-organised criticality through the lens of the Bak-Tang-Wiesenfeld sandpile model, explained for high schoolers.
Percolation
An introduction to percolation theory, phase transitions, and spanning clusters.
Diffusion-Limited Aggregation: Growing Fractals
An introduction to the mathematics of diffusion-limited aggregation, explaining how random walks and simple sticking rules create complex fractal geometries like lightning and coral.
Lindenmayer Systems: The Geometry of Growth
An interactive string-rewriting system initially conceived to model the growth of plants.
The SIR Epidemic Model
An introduction to the SIR epidemic model, explaining the mathematics of infectious disease spread and the Kermack-McKendrick compartmental model.
Lotka-Volterra Model
An introduction to the Lotka-Volterra predator-prey equations, explaining non-linear dynamics and ecological balance, explained for high schoolers.
Turing Patterns: How Chemistry Paints Biology
An introduction to reaction-diffusion systems and Turing patterns, explaining how simple math creates complex biological shapes for high schoolers.
Cloth Simulation: Verlet Integration in Practice
An introduction to Verlet integration and structural distance constraints used for simulating soft bodies and fabrics.
Buffon's Needle: Estimating Pi with Geometry
An introduction to Buffon
Galton Board: The Mathematics of Chance
An introduction to the Galton Board, the binomial distribution, and the Central Limit Theorem.
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A living notebook of small, precise simulations and engineering experiments.