SPH Fluid: From Wikipedia to 60 FPS
Smoothed Particle Hydrodynamics looked terrifying on paper — neighbour searches, kernel functions, pressure gradients. Here's how I went from zero understanding to a silky smooth 3D fluid simulation running fully in the browser.
Read post →🔧 Devlog Series
Polish Localization Phase 1: 89 New Pages, 3-Way Language Switcher & a 2247-URL Sitemap
MySimulator gains a Polish (/pl/) locale — homepage with FAQPage JSON-LD, sortable categories hub, 80 category landings, curated translations baked into the data layer, 3-way navbar cycling EN→UK→PL, and hreflang=pl wired into 174 existing pages.
Wave 61: Double Pendulum Ensemble, Viscoelastic Fluid & DFT/STFT Visualiser
30-member pendulum ensemble makes the butterfly effect quantitative via Lyapunov regression; interactive Maxwell/Kelvin-Voigt/SLS blob with stress relaxation and dynamic moduli; live DFT spectrum and scrolling STFT spectrogram for seven signal types. Platform at 559 simulations.
Wave 60: Duffing Oscillator, Network Science & Turing Diffusion
Duffing oscillator with real-time phase portrait and Poincaré sections showing the period-doubling road to chaos; three random-graph models (Erdős–Rényi, Barabási–Albert, Watts–Strogatz) with force-directed layout; Gray-Scott Turing morphogenesis with five pattern presets. Platform at 556 simulations.
Wave 59: Strange Attractors, Wolf-Sheep & Kuramoto
3D drag-to-rotate strange attractor visualizer for Lorenz, Rössler, Thomas and Halvorsen systems with RK4 integration; spatial agent-based wolf-sheep predator-prey ecology with population chart; Kuramoto coupled oscillators with order parameter phase transition. 553 simulations.
Wave 58: Galton Board, Belousov–Zhabotinsky & Turing Machine
Galton board Plinko simulator converging live to binomial / normal; Belousov–Zhabotinsky 3-state excitable medium with spiral and target waves; seven-state universal Turing machine with tape visualization and busy-beaver presets. 550 simulations live.
Wave 57: Lévy Flight, Diffusion-Limited Aggregation & Shallow Water
Lévy flight random walk with α-stable distributions and Cauchy / Gaussian comparison; DLA fractal with sticking probability; Saint-Venant shallow water equations with dam-break wave propagation. 547 simulations live.
Wave 56: Polarization of Light, Statistics t-Test & Battery Electrochemistry
Polarization states and Malus's law with birefringence; Student t-test visualizer with effect size, p-value and power curves; lithium-ion battery with charging / discharging Nernst-equation electrochemistry. 544 simulations live.
Wave 55: Polyhedra Explorer, Fish School 3D & SPH Dam Break
18-polyhedra Platonic / Archimedean solid explorer with Euler characteristic V−E+F=2; Boids fish school with 200 agents, predator shark and pseudo-3D depth layers; SPH dam break with Poly6 / Spiky kernels and pressure coloring. 541 simulations live.
Wave 54: Van der Pol Synchronization, Bacteria Colony & Genetic Evolution
Van der Pol coupled oscillator synchronization with limit cycles and frequency entrainment; spatial bacteria colony competition with nutrient diffusion and three cell types; genetic evolution with selection, mutation and crossover operators. 535 simulations.
Wave 53: Laminar-Turbulent Transition, Islamic Geometry & Boundary Layer
Reynolds number pipe-flow transition visualizer; parametric Islamic geometric tiling generator with 10 classic star patterns; Blasius flat-plate boundary-layer profile with displacement and momentum thickness. 532 simulations live.
Wave 52: Gambler's Ruin, Wiener Process & k-Fold Symmetry
Gambler's ruin random-walk with exact ruin-probability formula and ensemble histogram; Wiener process Brownian paths with configurable drift and diffusion; k-fold rotational symmetry generator with interactive spirograph patterns. 529 simulations.
Wave 51: Truchet Tiles, Benford's Law & Pipe Flow
Seeded Truchet tile mosaic generator with four colour themes and connectivity modes; Benford's Law explorer with seven real-world datasets and χ² fraud-detection statistic; Hagen-Poiseuille laminar pipe flow with animated velocity profiles. 526 simulations.
Wave 50: Complement Cascade, Spin Precession & Galvanic Cell
Animated complement system cascade with three activation pathways, C3b opsonization, and MAC pore formation; Larmor spin precession on an isometric Bloch sphere with T1/T2 relaxation; and a galvanic cell with Nernst-equation electrochemistry and five metal-pair presets. Platform at 523 simulations.
Wave 49: Membrane Transport, Van der Waals Gas & Grain Growth
Goldman-Hodgkin-Katz ion channel membrane potential with animated Na⁺/K⁺/Cl⁻ particles; real-gas P-V isotherms with Maxwell equal-area construction and phase envelope; and metallic grain microstructure coarsening with Hall-Petch yield strength analysis. Platform at 520 simulations.
Wave 48: Electrolysis, Liquid Crystal & Magnetic Levitation
Animated electrolytic cell with Faraday’s laws and three presets; nematic liquid crystal director field with Frank elastic relaxation and Fréedericksz threshold; and superconducting levitation with Meissner effect and force–height analysis. Platform at 517 simulations.
Wave 47: Electrode Kinetics, Polymer Chain & Magnetic Domains
Butler–Volmer electrode kinetics with Tafel plots and cyclic voltammetry; a freely-jointed polymer chain with Flory scaling and Monte Carlo sampling; and a 2D Ising model for magnetic domain formation and B–H hysteresis loops. Platform at 514 simulations.
Wave 46: Shape Memory Alloy, Adsorption Isotherm & Groundwater Flow
Austenite–martensite phase transformation and superelastic hysteresis in NiTi; Langmuir, BET, and Freundlich adsorption isotherms with animated surface coverage; and Darcy’s law groundwater flow with aquifer cross-section, equipotentials, and interactive pumping well drawdown. Platform at 511 simulations.
Wave 45: Galactic Rotation Curve, Herd Immunity & Population Genetics
Animated galactic rotation curve with NFW dark matter halo and Freeman disk; SIRV herd immunity with live vaccination threshold indicator; and Hardy–Weinberg population genetics with drift, selection and mutation. Platform at 508 simulations.
Wave 44: Derivative Visualizer, Holography & Superconductivity
Limit definition of derivative with animated h→0 secant convergence; wave-optics holography simulator with record/reconstruct modes; and BCS superconductivity with Cooper pairs, Meissner effect, and Type II vortex lattice. Platform at 505 simulations.
Wave 43: Brouwer Fixed Point, Dark Matter Halo & Cosmic Web
Brouwer Fixed Point Theorem visualised as a continuous map on a 2D disc; NFW dark matter halo density profile with rotation curve decomposition; and cosmic web large-scale structure via Zel’dovich approximation. Platform at 502 simulations.
Wave 42: Cytoskeleton, Cell Signaling & Immune Response
Three new cell biology simulations: actin treadmilling drives a crawling cell via myosin motors and focal adhesions; a MAPK/ERK signaling cascade shows how one ligand molecule triggers a thousand-fold amplified nuclear response via Hill kinetics; an agent-based immune model pits neutrophils, macrophages, T-cells, and antibodies against a replicating pathogen with vaccination effects. Platform at 499 simulations.
Wave 39: Law of Large Numbers, Fusion Reactor & Molecular Spectroscopy
Three new simulations spanning probability, plasma physics, and physical chemistry: LLN convergence with 8 distribution types and ±σ/√N bands, D–T fusion tokamak with Lawson criterion and Q-value gauge, and molecular IR absorption spectra for H₂O, CO₂, CH₄, HCl, NH₃ via Beer–Lambert law. Platform at 490 simulations.
Wave 38: Faraday’s Law, Power Grid & Photonic Crystal
Three new simulations across electromagnetism, power engineering, and photonics: Faraday Induction (bar magnet through coil, EMF oscilloscope, Lenz’s law arrow), Power Grid (DC power flow with Gauss-Seidel solver, cascade failure on ring/mesh/radial topologies), and Photonic Crystal (Transfer Matrix Method bandgap simulation, transmission spectrum, evanescent wave animation). Platform at 487 simulations.
Wave 37: SVD Compression, Z-Pinch & Potential Energy Surface
Three new simulations crossing linear algebra, plasma physics and physical chemistry: SVD Compression (rank-k image approximation with power-iteration SVD and singular-value bar chart), Z-Pinch (plasma column with Bennett equilibrium and sausage/kink MHD instabilities), and Potential Energy Surface (Müller-Brown PES with animated particle, friction & thermal noise). Platform at 484 simulations.
Wave 36: Ant Colony, Band Structure & Lorenz Waterwheel
Three new simulations spanning biology / CS, solid-state physics, and chaos theory: Ant Colony Optimization (ACO TSP solver with pheromone trails τα·ηβ roulette selection), Band Structure (semiconductor E-k diagram for Si/Ge/GaAs/Diamond with Fermi-Dirac curve and doping controls), and Lorenz Waterwheel (Malkus 12-bucket wheel + live butterfly phase portrait, RK4). Platform at 481 simulations.
Wave 35: Harmonograph, Sand Dune & Coral Reef
Three new simulations spanning math, earth science, and marine biology: Harmonograph (dual-pendulum progressive Lissajous drawing with 6 presets and 4 color modes), Sand Dune (aeolian saltation CA with avalanche rule and emergent barchan morphology), and Coral Reef (4-state temperature-driven CA with bleaching, death, and recovery dynamics). Platform at 478 simulations.
Wave 34: Rock Cycle, Supernova & Tidal Forces
Three new science simulations: Rock Cycle (interactive geological node diagram with 6 rock types, 11 bezier transition flows and 200 animated particles), Supernova (5-phase stellar lifecycle from main sequence to neutron star or black hole, element-coded ejecta), and Tidal Forces (Roche limit visualiser with live satellite deformation and debris ring formation). Platform at 475 simulations.
Wave 33: Tsunami, Satellite Constellation & Volcano
Three new simulations: Tsunami (2D Shallow Water Equations, seafloor-rupture trigger, shoaling at coast), Satellite Constellation (Walker Delta 3D orbital visualiser with Starlink, GPS, Galileo and Polar presets), and Volcano Eruption (Stromboli/Hawaiian/Vulcanian/Plinian particle eruption). Platform at 472 simulations.
Wave 32: DLA, Phase Portrait & Turing Patterns
Three new math simulations: Diffusion-Limited Aggregation (random-walk particles grow fractal trees with D ≈ 1.71), Phase Portrait (vector field, nullclines, RK4 trajectories for 6 classic 2D ODEs), and Turing Patterns (Gray-Scott reaction-diffusion: Spots, Stripes, Labyrinth, Mitosis, Worms). Platform at 469 simulations.
Wave 31: Newton's Fractal, Sand Pile & Complex Functions
Three new math simulations: Newton's Fractal (per-pixel Newton iteration for zn−1, basin colouring, zoom+pan), Sand Pile (Bak–Tang–Wiesenfeld SOC, avalanche power-law histogram), and Complex Functions (domain colouring, 12 functions, magnitude rings). Platform at 466 simulations.
Wave 30: Fourier Series, Gravitational Lensing & Epidemic Wavefront
Three new simulations: Fourier Series Builder (animated epicycle chains, analytic coefficients, live frequency spectrum), Gravitational Lensing (reverse ray-tracing, point-mass/SIS/NFW lens models, Einstein rings), and Epidemic Wavefront (reaction-diffusion SIR on 150×150 grid, R₀, Fisher-KPP wavefront speed). Platform at 463 simulations.
Wave 29: Taylor Series, Hodgkin–Huxley Neuron & Ising Model
Three new simulations: Taylor/Maclaurin series visualiser (analytic nth-derivative, adjustable expansion centre, error plot), Hodgkin–Huxley conductance neuron (Nobel 1963, Na⁺/K⁺ gating, action potential spikes), and 2D Ising model (Metropolis Monte Carlo, spontaneous magnetisation, Tc = 2.269 J/kB). Platform at 462 simulations.
Wave 28: Debye Shielding, Bayesian Updating & Fabry–Pérot
Three new simulations: plasma Debye shielding (Yukawa screened potential, λ_D, Debye sphere), Bayesian updating (Beta-Binomial conjugate, credible intervals, real-time posterior), and Fabry–Pérot interferometer (Airy resonances, FSR, finesse). Platform at 462 simulations.
Wave 27: Quantum Tunnelling, Fluid Vorticity & Game Theory
Three new simulations: exact 1D quantum tunnelling via transfer matrix (T(E) curve, double-barrier resonance), Kelvin–Helmholtz vortex sheet rollup (Biot–Savart, N vortices), and evolutionary spatial Prisoner’s Dilemma (ALL-D, ALL-C, TFT, GRIM, RAND strategies). Platform at 461 simulations.
Wave 26: Electromagnetism, Dark Matter & IS-LM Economics
Three new simulations: Electromagnetic Induction (Faraday’s law, moving magnet, AC generator), Galaxy Rotation Curves (NFW dark matter halo, flat curve vs Newtonian), and IS-LM Macroeconomic Model (fiscal & monetary policy shocks). Platform at 458 simulations.
Wave 25: Linear Algebra, Topology & Machine Learning
Three new simulations covering PCA & SVD visualiser (eigenvectors, explained variance), topological surface explorer (genus 0–3, Euler characteristic), and neural network decision boundary trainer. Plus spotlight and learning blog posts.
Wave 24: Gravitational Waves, Phase Equilibrium & Thermodynamics
Two new simulations: Gravitational Wave Chirp (0PN inspiral waveform, binary orbit animation, chirp mass readout, LIGO sensitivity context) and Chemical Equilibrium / Phase Equilibrium (G(Q) curve, ICE concentration bars, van’t Hoff plot). Spotlight on Fluid Dynamics & Turbulence; Learning post on Thermodynamics & Statistical Mechanics.
Wave 23: Topology, General Relativity & Cosmology
Two new simulations: PCA & SVD Visualiser (covariance matrix, real-time eigenvectors, explained variance bar chart) and Torus & Genus Explorer (genus 0–3 surfaces, Euler characteristic χ = 2−2g, Gauss-Bonnet). Spotlight on GR & Cosmology; Learning post on Complex Analysis.
Wave 22: Statistics, Special Relativity & Electrochemistry
Three simulations: relative simultaneity train thought experiment (dual-frame Lorentz animation), Nernst equation galvanic cell (animated ion migration, E vs ln Q graph), eigenvectors visualiser (unit circle–to–ellipse transform). Posts on statistics & probability and differential equations in physics.
Wave 21: Cell Biology, Crystal Structures, Relativity & Linear Algebra
Three deep-dive posts: cell biology and biophysics (lipid bilayers, osmosis, mitosis, motor proteins, ion channels); crystal structures 3D (BCC/FCC/HCP, painter’s algorithm); linear algebra for scientists (SVD, PCA, spectral theorem). Plus osmosis, aurora, moon phases, twin paradox, Lorentz contraction, Möbius strip, matrix transforms and Fibonacci spiral.
Wave 20: Immunology, Statistical Field Theory, Geophysics & Video Thumbnails
Three deep-dive posts: immune system architecture and mRNA vaccines; statistical field theory from Ising models to the renormalisation group and diffusion models; geophysics and seismology. Plus a Playwright screenshot pipeline generating OG images for 345 simulations.
Wave 19: Cosmology, General Relativity, Physical Chemistry & PWA Offline-First
Three deep-dive posts: CMB acoustic peaks and dark matter N-body, curved spacetime and Kerr black holes, Marcus electron transfer and femtochemistry. Plus full 345-sim PWA precache, search term highlighting, and JSON-LD structured data audit.
Wave 18: Plasma Physics, Topology, Materials Science & Fuzzy Search
Three deep-dive posts: tokamak confinement and the NIF ignition milestone, persistent homology and knot theory, dislocations and graphene Dirac cones. Plus Levenshtein fuzzy search, pinch-zoom canvas and Service Worker v18.
Wave 17: Number Theory, Statistical Mechanics, Neuroscience & Search 2.0
Three deep-dive posts: prime number theorem and post-quantum cryptography, Ising model and the renormalization group, Hodgkin-Huxley neural circuits. Plus a full inverted-index Search 2.0 with tag facets and difficulty levels.
Wave 16: Astrophysics, Turbulence, Cell Biology & A11y Audit
Stellar evolution to gravitational waves, Kolmogorov turbulence cascade, molecular machines in the cell. Plus a full WCAG 2.2 AA accessibility audit, keyboard navigation and reduced-motion fixes.
Wave 15: Quantum Information, Electromagnetism, Climate Science & Platform UX
Three deep-dive posts shipped. Plus: search UX overhaul, simulation glossary, JSON-LD structured data roll-out, categories taxonomy redesign, and a third-anniversary retrospective.
Wave 14: Acoustics, Thermodynamics, Plasma — and the Road to 350 Simulations
Three deep-dive posts shipped. Plus: platform stats approaching 350 simulations, the writing process behind each wave, and a preview of Wave 15 — quantum information, electromagnetism, and climate science.
Wave 13 & Simulations in the Classroom — Materials Science, General Relativity and Topology
Three deep-dive posts shipped. Plus: which simulations appear in university syllabi, how educators use pre-lecture and in-class demo patterns, and the sharable-link feature roadmap.
Wave 12 Content Sprint — Special Relativity, Ecology, Statistics, Algorithms, Cosmology and Linear Algebra
Six deep-dive posts in five weeks: the topics chosen, what changed in the writing process, blog series status after 82 posts, and what Wave 13 will bring.
345 Simulations — Relativity, Topology, Ecology and the Push to Full Science Coverage
New categories launched: special relativity, topology, ecology, algorithms. Five hardest simulations, architecture reflections, and the road to 400.
2027 Year in Review — Waves Delivered, Platform Stats, and the 2028 Roadmap
345+ simulations, 80+ categories, four content waves shipped. Chemistry and agent-based collections launched. Q1 2028 roadmap: Plasma & Materials, Numerical Methods, and a simulation glossary.
60 FPS on Every Device — Performance Engineering for Browser Simulations
Fixed timestep, spatial hash collision, Web Worker offloading and battery-aware throttling: 47 slow simulations brought to 60 FPS.
Q3 2027 — Genetics Spotlight, Statistical Mechanics Guide and the Q4 Roadmap
Wave 9 shipped: Spotlight #19 on Genetics & Molecular Biology, Learning #18 on Statistical Mechanics, 65 blog posts total.
Q2 2027 — Wave 8 Content, Electronics & Quantum Deep Dives, and What's Next
Wave 8 shipped: Spotlight #18 on Electronics, Learning #17 on Quantum Mechanics, 345+ sims, 80+ categories, and the Q3 roadmap.
Applied Science — Five New Categories for Engineering, Ecology and Combinatorics
How we designed and launched five new simulation categories: Ecology, Civil Engineering, Agronomy, Combinatorics, and Chronobiology.
Spring 2027 — 345 Simulations, Relativity Category and 30+ New Additions
Special relativity, ecology, mathematical biology, civil engineering, and agronomy simulations — everything shipped this quarter.
Client-Side Search — Inverted Index, Trie and URL State for 350 Pages
28 kB index, sub-10 ms queries, prefix autocomplete and shareable search URLs — no server, works fully offline.
350 Simulations Milestone — New Optics, Earth Sciences and Materials Categories
We crossed 350 interactive simulations. Three new categories, community growth stats, and what shipped this quarter.
Devlog #22 — WebGPU Compute Shaders in Production: 50× Faster Physics
Migrating Lattice-Boltzmann and SPH fluid sims from JavaScript to WebGPU compute shaders — WGSL code, buffer alignment pitfalls, and a clean fallback to WebGL for unsupported browsers.
Devlog #21 — 300 Simulations: Engineering Lessons from 2.5 Years
What we learned building 300 browser simulations — the 5 hardest projects, 4 architecture decisions we got right, 2 we got wrong, and the road to 500.
Devlog #20 — Building an Automated i18n Pipeline for 250+ Pages
How we automated Ukrainian translation across 250+ HTML pages — BeautifulSoup slot extraction, MT + post-edit review, glossary protection, and hreflang injection.
Devlog #19 — Going Offline-First: PWA Service Worker Architecture
100 Lighthouse PWA score, 0 ms repeat navigation, 200+ precached pages — the cache strategies, install prompt, and background sync that make mysimulator.uk work without internet.
250 Simulations: Lessons from Building the Biggest WebGL Physics Library
Two years, 250 sims, 73 categories. What worked, what we'd do differently, and the 10 hardest simulations we shipped.
Building Instant Search & Category Filtering for 250+ Sims
Inverted index, trie auto-complete, bitmask category filtering, and URL state serialisation — zero dependencies, <5 ms search.
Building the Bridge Designer: FEM in the Browser
Stiffness matrix assembly, Gaussian elimination in JavaScript, and real finite-element truss analysis — colour-coded stress in real time.
Making Simulations Work on Mobile: Touch, Performance & Battery
Pointer events API, adaptive quality presets, lazy Three.js loading, iOS viewport quirks, and battery-aware throttling — how we got 3× better FPS on mid-range phones.
When a Simulation Becomes a Thinking Tool
The moments our own physics engine taught us something unexpected — ballistics, chaotic pendulums, disease spread, and bridge design.
First Accessibility Audit: What We Found and Fixed
WCAG 2.1 AA audit: keyboard traps in canvases, missing labels, contrast failures, and no skip-to-content link. 18 violations, all addressed.
225 Simulations & Plans for 300
The 225-sim milestone: breakdown by category, what we learned, and a quarter-by-quarter roadmap toward 300 simulations by end of 2026.
Adding Ukrainian in 4 Days
No CMS, no translation API — just Python scripts, careful hreflang, and a language switcher built from scratch. How we shipped 293 Ukrainian pages in a single sprint.
212 Simulations in a Year: How the Library Grew
From 40 simulations in early 2025 to 212 by March 2026 — how the library grew, the Canvas 2D vs Three.js decision, the hardest categories, Ukrainian translations, and what's next.
100 Simulations Milestone: Rocket Launch & Atmospheric Re-entry
How the project hit 100 browser simulations with two aerospace additions — Tsiolkovsky's rocket equation in action and a physically-accurate re-entry heatshield model with four outcomes.
Three New Tutorials: Solar System, GLSL Shaders & localStorage
The tutorial section grew from 8 to 11 — a Three.js solar system for intermediates, raw GLSL fire-and-water shaders for the brave, and a beginner-friendly localStorage guide. Plus related-sim cross-links on 16 articles.
Reaction-Diffusion — Turing Patterns on the GPU
How Alan Turing's 1952 morphogenesis equations became a real-time WebGL texture shader. Ping-pong framebuffers, the Gray–Scott model, and the haunting patterns that emerge from two chemicals.
Boids — 3 Rules, Emergent Behaviour & 10,000-Bird Skies
Craig Reynolds' three steering forces — separation, alignment, cohesion — are all it takes to fill the sky with a convincing murmuration. Plus the spatial hash that makes 10,000 agents fast.
Ocean Shader — GLSL, Gerstner Waves & Fresnel in 3 Days
Realistic ocean water with animated vertex displacement, foam at crests and a Fresnel reflection effect — all written from scratch in GLSL over a long weekend.
Galaxy — Rendering 80,000 Stars Without Slowdown
A spiral galaxy with 80 k stars sounds impossible at 60 FPS — until you discover InstancedMesh and custom instanced shaders. The full story of how I cut GPU draw calls from 80,000 to 1.
Tectonic Plates — Spherical Geometry & Real Displacement
Mapping Earth's crustal plates onto a sphere with displacement maps and smooth boundary animations. Three.js, spherical harmonics and a lot of trigonometry.
SPH Fluid — from Wikipedia to 60 FPS
SPH neighbour lookups, kernel functions, pressure and viscosity forces — translating dense academic notation into running JavaScript code. Plus the spatial-hash optimisation that made it real-time.
How This Project Started — One Simulation in a Weekend
It was supposed to be a quick Three.js experiment for a weekend. A year and 40+ simulations later, here we are. The origin story of 3D Simulations.
📣 Announcements
New: Earth Sciences — Seismic Waves, Volcanoes, Mantle Convection and Polar Ice
Ten interactive Earth Sciences simulations — the most-requested new category from our community.
New: Optics & Light Expanded — Total Internal Reflection, Water Caustics and Five More
Seven optics simulations live — two brand new (TIR, Water Caustics), five rebuilt with deeper physics content.
New: Biology Simulation Suite — 8 Interactive Life Science Simulations
Boids flocking, ant pheromone trails, predator-prey cycles, genetic algorithms, protein folding, evolutionary game theory, cellular automata — all in your browser.
New: Quantum Simulation Suite Expanded — 6 Interactive Simulations
Bloch sphere qubit, quantum circuit builder, Bell state entanglement, spin precession, quantum tunneling, and Grover's search — all live in the browser.
New & Expanded: Fluid Dynamics Collection
Lattice-Boltzmann D2Q9, Kármán vortex street, Bénard convection, blood flow, Gerstner ocean waves — 6 sims powered by real CFD and finite-element methods.
New Category: Electromagnetism Simulations
Eight new EM simulations — electric field Coulomb solver, Biot-Savart magnetic fields, Faraday's law, RLC phasors, FDTD EM waves, antenna patterns, AM/FM modulation, and digital filters.
New: Cryptography & Game Theory Simulations
RSA encryption, AES step-by-step, SHA-256, prisoner's dilemma tournament, auction theory, and evolutionary game dynamics — 8 new simulations.
New: Environment & Energy Simulations
Solar panel IV curves, wind turbine Betz limit, nuclear fission, carbon cycle, tidal energy, greenhouse effect — 8 new physics simulations.
New: Transport & Society Simulations
Bus bunching, pedestrian flow, NaSch traffic, voter model, income inequality — 9 new sims across 2 new categories, now live in EN + UA.
New: Medicine & Rehabilitation Simulations
Cardiac action potentials, drug diffusion, blood flow, and brainwave oscillations — physics-based tools for medical education.
Kids Science Categories Are Live — Magic, Space & More
Three new simulation categories for ages 6–12: Magic of Physics, Space for Kids, and Kids Chemistry. Simple controls, wonder-first design.
New Categories 2026 — Materials Science, Data Viz & Cosmology
Three new simulation categories in development for 2026: crystal structures and phase diagrams; spectrograms and force-directed graphs; Big Bang nucleosynthesis and CMB models.
New: AI & ML, Robotics & Economics — Three More Categories
AI/ML (neural networks, Q-learning, SOM), Robotics (FABRIK IK, drone swarm, hexapod) and Economics (Solow model, income inequality, opinion dynamics) — 19 new simulations, all EN + UK.
New: Quantum Computing, Cryptography & Nuclear Physics
Three complete new categories: Bloch sphere, Grover's algorithm, RSA key exchange, elliptic curves, fission chain reactions, and the Bethe-Weizsäcker binding-energy curve — 14 new simulations.
New Category: Weather & Atmosphere — Tornado, Rain, Rainbow & More
Six new interactive simulations covering Earth's most dramatic atmospheric processes: tornado vortex, rain physics, rainbow optics, atmosphere layers, wildfire spread, and hurricane formation.
Categories Launch — Organising 40+ Simulations
Physics, Nature, Algorithms, Chaos, Space and more — introducing the new category system that brings order to the whole project. Plus dedicated Kids sections with age ratings!
Coming Soon: Quantum Physics Category
Wave–particle duality, quantum tunnelling, the double slit experiment and Schrödinger's equation — visualised in the browser. Watch this space!
Game of Life Update — Spherical Mode & 3 New Rulesets
Conway's classic gets a 3D sphere mode, custom ruleset editor and colour-coded cell age. Try the "Highlife" and "Day & Night" rules!
New Category: Algorithms — A*, Sorting & Mazes
A dedicated Algorithms section lands with A* pathfinding, bubble/quick/merge sort visualisers, maze generators and the Travelling Salesman Problem. Six interactive demos, all with step-by-step animation.
🔭 Category Spotlight
Chaos Divergence, Rheology & Signal Analysis
Lyapunov exponents measured via double-pendulum ensemble regression; Maxwell and Kelvin-Voigt viscoelasticity — Deborah number, complex modulus G′/G″, stress relaxation; DFT spectral leakage and window functions; STFT spectrogram and the time-frequency uncertainty principle.
Chaos, Network Theory & Morphogenesis
Duffing oscillator Poincaré sections and the period-doubling cascade to chaos; scale-free and small-world graph topology in three random-graph models; Turing's 1952 reaction-diffusion instability and the Gray-Scott morphogenesis landscape.
Chaos, Ecology & Neuroscience
Strange attractors, fractal topology and Lyapunov exponents in four chaotic systems; agent-based predator-prey ecology generating Lotka-Volterra cycles from local rules; Kuramoto synchronization phase transition in coupled neural oscillators.
Probability, Chemistry & Algorithms
Galton board and the central limit theorem convergence; BZ reaction excitable-medium spiral waves explained by Greenberg–Hastings automata; Turing machine computation and universality with busy-beaver halting analysis.
Probability, Generative Art & Fluid Dynamics
Lévy stable distributions and anomalous superdiffusion; DLA fractal growth by diffusion-limited aggregation; Saint-Venant shallow water equations and dam-break shock front dynamics.
Optics, Statistics & Electrochemistry
Polarization states, Malus's law and birefringent optics; Student t-test with effect size and statistical power curves; lithium-ion battery charge-discharge electrochemistry and Nernst-equation thermodynamics.
Geometry, Swarm Intelligence & Fluid Dynamics
Platonic and Archimedean solids with Euler characteristic V−E+F=2; emergent fish-school Boids dynamics with predator-avoidance behaviour; SPH dam break illustrating Navier-Stokes pressure and viscosity forces in real time.
Immunology, Magnetism & Electrochemistry
Complement-system immunity with three activation pathways, DAF regulation, and MAC pore formation; Larmor precession and MRI spin physics; galvanic cell electrochemistry and Nernst-equation thermodynamics. Three underrepresented categories, each now with three simulations.
Immune Cascades, Spin Physics & Electrochemistry
9-step guide connecting complement cascade immunology, Larmor spin precession and Bloch-equation MRI physics, and Nernst-equation galvanic cell thermodynamics through their shared exponential kinetics and regulatory feedback mechanisms.
Cell Biology, Physical Chemistry & Materials Science
Ion channels and Goldman-Hodgkin-Katz membrane biophysics; van der Waals real-gas equation, Maxwell construction, and the liquid-vapour critical point; metallic grain growth kinetics and Hall-Petch strengthening. Three underrepresented categories, each now with three simulations.
From Ion Channels to Grain Growth
9-step guide connecting membrane biophysics, real-gas thermodynamics, and metallic microstructure through their shared mathematics: Nernst equation, GHK potential, van der Waals cubic, Maxwell construction, Arrhenius kinetics, and Hall-Petch strengthening.
Immunology & Infectious Disease — Immune Architecture, Vaccine Mechanisms and Epidemic Dynamics
Innate immunity and toll-like receptors, T-cell V(D)J recombination and MHC presentation, B-cell affinity maturation, mRNA vaccine platforms, herd immunity threshold h_c=1−1/R&sub0;, SEIR epidemic modelling, and checkpoint immunotherapy.
Electrochemistry & Materials Interfaces
9-step rigorous guide: electrode double layer and Debye screening; Nernst equation; Butler–Volmer kinetics and Tafel analysis; Faraday’s laws; liquid crystal order parameter and Frank elastic energy; Fréedericksz transition; polymer Flory scaling; BCS superconductivity and Meissner levitation.
Fluid Mechanics & Transport in Porous Media
Navier–Stokes equations, viscosity and Reynolds number; Bernoulli’s principle; boundary layers and turbulence; Darcy’s law in porous media; groundwater flow equations; and advection–diffusion transport. A self-contained guide from pipe flow to aquifer hydrogeology.
Electrochemistry & Soft Matter — Interfaces, Liquid Crystals & Polymers
Nernst equation and Butler–Volmer kinetics; Faraday’s electrolysis laws; nematic order parameters; Frank elastic free energy; Fréedericksz transition; polymer chain conformations and Flory exponents.
Materials Science & Engineering — From Crystal Lattices to Smart Alloys
Crystal lattices and diffraction; alloy phase diagrams and the lever rule; shape memory alloys and superelasticity; BCS superconductivity; band structure and semiconductors; stress–strain curves, fracture mechanics, and creep.
Electromagnetism & Maxwell’s Equations — A Guided Learning Path
Coulomb and Gauss for electrostatics; Biot-Savart and Ampère for magnetostatics; Faraday induction and Lenz’s law; Maxwell’s displacement current; the EM wave equation (c = 1/√(μ0ε0)); Poynting vector; LC oscillators and transformers; Lorentz covariance and the field tensor Fμν.
Galaxies, Rotation Curves & Dark Matter — The Hidden Mass of the Universe
Vera Rubin’s flat rotation curves; NFW halo profile (ρ ∝ r−1(1+r/rs)−2); Freeman disk and bulge decomposition; Bullet Cluster; gravitational lensing (Einstein rings); CMB baryon/DM ratio; WIMP, axion and PBH candidates; MOND and the Tully-Fisher relation; ΛCDM tensions.
Electromagnetism & Maxwell’s Equations — Faraday, Lenz, and the Unification of Light
Faraday’s 1831 induction discovery; Lenz’s law and energy conservation; the four Maxwell equations (Gauss, Faraday, Ampère-Maxwell); displacement current; EM wave equation at speed c; AC generators (NBAω); transformers; eddy currents; EM spectrum; Larmor radiation; plasma and the Lorentz force; Fμν tensor formulation.
Fluid Dynamics & Turbulence — Navier-Stokes, Reynolds and the Kolmogorov Energy Cascade
Navier-Stokes equations and the Millennium Prize Problem; Reynolds number and the laminar-to-turbulent transition; Bernoulli and Kutta-Joukowski lift; Blasius boundary layer; von Kármán vortex street (Strouhal number, Tacoma Narrows); Kolmogorov −5/3 cascade; compressible flow and shocks; Buckingham Π theorem; quantum turbulence in superfluids.
General Relativity & Cosmology — Curved Spacetime, Black Holes and the FLRW Universe
Equivalence principle, metric tensor, Einstein field equations; Schwarzschild geometry (event horizon, photon sphere, ISCO); Kerr metric & Penrose process; gravitational lensing (Eddington 1919, Einstein rings); FLRW metric, Friedmann equations, CMB, Planck 2018; dark energy and the cosmological constant problem.
Statistics & Probability — Distributions, Bayesian Inference and Markov Chains
Binomial, Poisson, Normal, Beta and Gamma distributions; Central Limit Theorem (Lindeberg, Berry-Esséen); hypothesis testing, p-values, Type I/II errors, Bonferroni and BH corrections; Bayesian inference with conjugate priors and MCMC; Markov chains and PageRank; MLE and the Cramér-Rao bound.
Cell Biology & Biophysics — Lipid Bilayers, Osmosis, Mitosis and Ion Channels
Lipid bilayer Singer-Nicolson model and Helfrich bending energy, van ’t Hoff osmotic pressure equation, cytoskeleton persistence lengths, mitosis phases and spindle assembly checkpoint, kinesin/myosin/dynein motor proteins, Hodgkin-Huxley ion channel equations.
Geophysics & Seismology — Earth’s Interior, Seismic Waves, Plate Tectonics and the Geomagnetic Dynamo
PREM interior model, P- and S-wave velocities and shadow zones, moment magnitude M_w and Gutenberg-Richter, mantle convection driving plate tectonics, GRACE geoid and isostasy, and the MHD geomagnetic dynamo with palaeomagnetic reversals.
Cosmology & Dark Matter — CMB, Inflation, N-Body Simulations and Large-Scale Structure
Inflationary slow-roll and the primordial power spectrum, CMB acoustic peaks and Sachs-Wolfe effect, NFW dark matter halos, Press-Schechter mass function, baryon acoustic oscillations as a standard ruler, DESI BAO 2024 results.
Physical Chemistry & Reaction Dynamics — Transition States, Marcus Theory, Spectroscopy and Femtochemistry
Eyring TST and tunnelling corrections, Marcus inverted region and photosynthetic electron transfer, Clapeyron phase equilibria, IR/Raman/NMR selection rules, DFT Kohn-Sham equations, and femtosecond wavepacket spectroscopy.
Plasma Physics & Fusion — Tokamak Confinement, Lawson Criterion, MHD Stability and ICF
Debye shielding length, tokamak safety factor, Lawson fusion triple product and ITER targets, kink and tearing MHD instabilities, Alfvén waves, and the 2022 NIF ignition milestone.
Materials Science — Dislocations, Phase Diagrams, Semiconductor Bands and Nanomaterials
Crystal defects and Hall-Petch strengthening, binary eutectic phase diagrams, Bloch band theory, polymer Flory-Huggins thermodynamics, graphene Dirac cones and superparamagnetism.
Neuroscience & Neural Circuits — Hodgkin-Huxley, Synaptic Plasticity and Whole-Brain Models
Conductance-based action potentials, quantal synaptic release, STDP Hebbian learning, Kuramoto oscillator synchronisation, connectome graph theory, and The Virtual Brain platform.
Number Theory & Cryptography — Primes, RSA, Elliptic Curves and Post-Quantum Security
Prime number theorem, Riemann hypothesis, modular arithmetic, RSA and ECDSA mechanics, NIST PQC finalists CRYSTALS-Kyber and Dilithium, and Schnorr zero-knowledge proofs.
Cell Biology & Molecular Machines — DNA Replication, Protein Folding, ATP Synthase and CRISPR-Cas9
Semi-conservative replication error rates, Anfinsen energy funnels and AlphaFold2, ATP synthase rotary motor, cytoskeletal dynamic instability, and CRISPR-Cas9 PAM search kinetics.
Astrophysics & Stellar Evolution — HR Diagram, Stellar Structure, Supernovae and Gravitational Waves
Hertzsprung-Russell diagram, polytrope models, pp chain and CNO cycle, core-collapse supernova mechanics, neutron star cooling, and the chirp mass formula behind LIGO detections.
Climate Science — Radiative Forcing, Feedback Loops, Carbon Cycle and Tipping Points
Greenhouse energy balance, climate feedback decomposition, global carbon cycle fluxes, tipping element thresholds, atmospheric Hadley-cell circulation, and the CMIP6 model hierarchy.
Quantum Information & Computing — Qubits, Entanglement, BB84 and Quantum Algorithms
Bloch sphere state space, Bell inequality and CHSH bound, BB84 quantum key distribution, universal gate sets, Grover O(√N) search, and Shor’s polynomial-time factoring.
Plasma Physics — Debye Shielding, Particle Drifts, Aurora and Tokamak Fusion
The fourth state of matter: Debye length, cyclotron orbits, guiding-centre drifts, aurora formation at altitude, Lawson criterion, and MHD Alfvén waves — four interactive simulations.
Acoustics & Music Physics — Standing Waves, Chladni Patterns, Room Modes and Cochlear Mechanics
From pipe harmonics and Chladni plate eigenfrequencies to Sabine RT60, von Békésy travelling waves, and QRD diffuser design — six deep dives, five interactive simulations.
Topology — Möbius Strips, Klein Bottles, Knots and Minimal Surfaces
Euler characteristic, one-sided surfaces, non-orientable manifolds, knot polynomials, minimal surfaces and the topology of phase space — six simulations, six deep dives.
Materials Science — Crystals, Dislocations, Phase Diagrams and Semiconductor Bands
BCC/FCC/HCP lattices, Fick diffusion, Hall-Petch strengthening, Burgers vectors, eutectic diagrams, Fermi-Dirac distribution and nine interactive simulations.
Cosmology & the Universe — Big Bang, CMB, Dark Matter and Hubble Expansion
Six simulations across the full cosmic timeline: nucleosynthesis, CMB acoustic peaks, dark matter rotation curves, gravitational lensing and Hubble's law.
Ecology & Population Dynamics — Predator-Prey Cycles, Food Webs, Trophic Cascades and the Carbon Cycle
Lotka-Volterra oscillations, multi-species food webs, keystone predators, biological pump, global carbon cycle and collective flocking behaviour.
Algorithms & Combinatorics — Sorting, N-Queens, Graph Colouring, Collatz and Pascal's Triangle
Big-O complexity visualised, N-queens backtracking, DSatur graph colouring, Riemann integration, the Collatz conjecture and hidden identities in Pascal's triangle.
Statistics & Probability — CLT, Bayesian Inference, Markov Chains and Bootstrap Resampling
Central limit theorem demos, Bayesian prior-to-posterior updates, birthday paradox, linear regression, Maxwell-Boltzmann and bootstrap confidence intervals.
Chemistry & Chemical Kinetics — Reaction-Diffusion, Combustion, Acid-Base and Crystal Growth
Gray-Scott Turing patterns, Arrhenius chain-branching combustion, Henderson-Hasselbalch titration, DLA crystal growth, pharmacokinetics and the global carbon cycle.
Thermodynamics & Heat Transfer — Carnot, Blackbody Radiation and Phase Diagrams
Newton's cooling, Carnot efficiency bound, Maxwell-Boltzmann distributions, Planck spectrum, Bénard convection and binary alloy phase diagrams.
Genetics & Molecular Biology — DNA, Mendelian Inheritance, Cell Division and CRISPR
DNA replication fork, Mendelian Punnett squares, mitosis and meiosis, Michaelis-Menten kinetics and CRISPR-Cas9 gene editing.
Electronics & Digital Systems — Logic Gates, Transistors, ADC/DAC and Signal Processing
Logic gates, 8-bit adder, BJT/MOSFET transistors, RC filters, ADC/DAC, OFDM and phase-locked loops — the complete electronics collection.
Ecology & Life Systems — Food Webs, Trophic Cascades and Population Dynamics
Lotka-Volterra predator–prey cycles, trophic cascades, circadian rhythms, Brownian motion — interactive ecology simulations explained.
Special Relativity — Time Dilation, Lorentz Contraction and Spacetime Diagrams
Twin paradox, Minkowski diagrams, Lorentz contraction, E=mc², gravitational lensing — 6 interactive relativity simulations.
Chaos & Nonlinear Dynamics — Lorenz, Bifurcations and Turing Patterns
Lorenz attractor, bifurcation diagrams, Rössler, Van der Pol, double pendulum, Gray-Scott reaction-diffusion — 7 chaos sims.
Optics & Light — Snell's Law, Total Internal Reflection, Caustics and Diffraction
From Snell's law to GPU water caustics — 11 interactive optics simulations covering geometric, wave and quantum optics.
Quantum Computing — Qubits, Circuits, Entanglement & Grover's Algorithm
Bloch sphere, quantum gates, Bell states, Crank-Nicolson tunneling, and Grover's O(√N) search — six interactive simulations with the maths behind each one.
Fluid Dynamics — LBM, Navier-Stokes, SPH & Ocean Waves
D2Q9 Lattice-Boltzmann, Kármán vortex street, SPH particles, Bénard convection, blood flow, and Gerstner ocean waves — eight interactive CFD simulations.
Neuroscience & Medicine — Hodgkin-Huxley, MRI & Cardiac Models
Action potentials, spiking neural networks, brainwave oscillations, MRI Bloch equations, drug diffusion, and blood flow — 8 sims covering the maths of biology.
Electromagnetism — Maxwell's Equations, FDTD & EM Waves
Electric and magnetic fields, Faraday's law, RLC circuits, FDTD wave propagation, antenna-pattern Hertzian dipoles, and Fraunhofer diffraction — 10 sims explained.
Economics & Society — Game Theory, Crypto & Urban Growth
Bank runs, Bitcoin mining, bus bunching, Diffie-Hellman, decision trees, and blackjack strategy — the maths behind markets and society.
Chemistry & Materials — Crystal Growth, Reaction-Diffusion & More
Metropolis Monte Carlo, Gray-Scott reaction-diffusion, nuclear binding energy, and Young-Laplace surface tension — 8 sims, all algorithms explained.
Space & Astronomy — 12 Sims, from Orbits to Re-entry
N-body gravity, Tsiolkovsky rocket equation, atmospheric re-entry, asteroid deflection, and Doppler light shifts — all in the browser.
Physics & Mechanics — 18 Sims, Every Algorithm Explained
RK4 integration, Verlet pendulums, FEM trusses, SPH fluids, orbital mechanics — the biggest category on the site, fully mapped.
Climate & Ecology — 11 Sims Explained
Carbon cycle, disease spread, cyclone dynamics, ant colony optimisation — a guide to every climate and ecology simulation on the site.
Rendering & Generative Art — 13 Sims Explained
DLA, Gray-Scott reaction-diffusion, IFS fractals, ray marching SDF — the most visually striking simulations on the site, explained from the maths up.
Biology & Life Sciences — 12 Sims Explained
Boids flocking, genetic drift, protein folding, cardiac action potentials — a guided tour of every biology simulation with learning paths for different levels.
Quantum Physics & Computing — 10 Sims Explained
From the double-slit experiment to Grover's algorithm — a complete walkthrough of the quantum category with recommended learning paths for students and educators.
Math & Algorithms — 11 Sims Explained
Sorting visualisers, fractal generators, Voronoi diagrams, and the Travelling Salesman Problem — a guided tour of the entire Math & Algorithms category.
📖 Learning With Simulations
Thermodynamics & Statistical Mechanics — Entropy, Free Energy and the Boltzmann Distribution
Four laws of thermodynamics; Boltzmann entropy S=k_B ln W and the arrow of time; Carnot efficiency and Kelvin-Planck; thermodynamic potentials (U, A, H, G) and Maxwell relations; partition function and Boltzmann distribution; canonical and grand-canonical ensembles; phase transitions, Ising model & critical exponents; Bose-Einstein and Fermi-Dirac statistics; Landauer principle and Maxwell’s demon.
Complex Analysis in Physics & Engineering — Residues, Conformal Maps and Applications
Complex numbers & Argand plane; Cauchy-Riemann equations & analytic functions; Cauchy integral formula; Laurent series & residue theorem (classic integrals); conformal maps (Möbius, Joukowski aerofoil lift L=ρUΓ); 2D fluid flow, AC impedance phasors, Riemann zeta function & hypothesis.
Differential Equations in Physics — ODEs, PDEs, Phase Planes and Chaos
First-order ODEs (separation of variables, integrating factor, logistic growth); second-order oscillators (underdamped, overdamped, resonance, Q factor); phase plane analysis and Lotka-Volterra; PDEs (wave equation d’Alembert, heat equation Fourier series, Laplace); RK4 derivation; Lorenz attractor, Lyapunov exponent and Feigenbaum δ≈4.669.
Linear Algebra for Scientists — Matrices, Eigenvectors, SVD and PCA
Matrices as linear maps and basis change, determinants as signed volume scaling, eigenvalues and the characteristic polynomial, spectral theorem for symmetric matrices and its role in quantum mechanics and normal modes, SVD and the Moore-Penrose pseudoinverse, PCA and variance-maximising projections.
Statistical Field Theory — From Ising Models to Renormalisation and Deep Learning Connections
Landau-Ginzburg free energy and spontaneous symmetry breaking, Feynman path integrals Z=∫Dφe^−S[φ], Wilson RG fixed points and universality classes, 2D CFT and the Virasoro algebra, Boltzmann machines, score-based diffusion models.
General Relativity & Curved Spacetime — From the Equivalence Principle to Black Holes
Geodesic equation and Christoffel symbols, Riemann and Einstein tensors, Schwarzschild metric and orbital precession, gravitational wave quadrupole formula (LIGO GW150914), Kerr ergosphere, Hawking radiation and the information paradox.
Topology & Manifolds — Homotopy, Knot Theory, Homology and TDA
Topological spaces and homeomorphisms, π&sub1; van Kampen theorem, surface classification by Euler characteristic, Jones polynomial for knots, Betti numbers and persistent homology for data analysis.
Statistical Mechanics & Phase Transitions — Partition Functions, Ising Model and Renormalization
Boltzmann partition functions, Onsager’s exact 2D Ising solution (β = 1/8), Landau order-parameter theory, Wilson’s renormalization group, fluctuation-dissipation theorem and Metropolis Monte Carlo.
Fluid Dynamics & Turbulence — Navier-Stokes, Reynolds Decomposition, Boundary Layers and the Kolmogorov Cascade
From laminar pipe flow to the −5/3 energy spectrum: Reynolds number, Blasius boundary layers, Kelvin-Helmholtz instability, RANS k-ε closure, and Kolmogorov’s universal turbulence theory.
Electromagnetism — Maxwell’s Equations, EM Waves, Antennas and Transmission Lines
All four Maxwell equations, Poynting vector, Faraday induction, Hertzian dipole radiation, skin depth in conductors, and transmission-line SWR and the Smith chart.
Thermodynamics — From Heat Engines to Statistical Mechanics
Four laws, Clausius-to-Boltzmann entropy, Carnot efficiency, Maxwell-Boltzmann distribution, Maxwell's Demon and Landauer's principle, and Ising-model universality at phase transitions.
General Relativity — Spacetime, Gravity and Black Holes
Lorentz factor, Schwarzschild metric, ISCO orbits, gravitational redshift, GPS corrections, Einstein rings, gravitational wave quadrupole formula and LIGO strain.
Linear Algebra & Data Science — Matrices, Eigenvectors, Regression and Machine Learning
Matrix transformations, OLS regression geometry, Bayesian base-rate fallacy, K-Means Voronoi partition, gradient descent loss landscapes and convolutional network feature extraction.
Special Relativity — Time Dilation, Length Contraction, Minkowski Diagrams and the Twin Paradox
Einstein's two postulates, Lorentz transformation, γ-factor, proper time, barn-pole paradox, invariant interval, E=mc² and GPS relativistic corrections.
Agent-Based Modelling — Flocking, Epidemics, Ant Colonies and Emergent Traffic
Boids three-rule flocking, SIR epidemic R₀ and herd immunity, Lotka-Volterra predator-prey, ant pheromone ACO, bus bunching headway instability, and city growth cellular automata.
Algorithms & Computational Complexity — Sorting, Pathfinding and NP-Hard Problems
Big-O notation, sorting algorithms, Dijkstra vs A* pathfinding, N-Queens backtracking, Traveling Salesman 2-opt, and genetic algorithms.
Statistical Mechanics & Thermodynamics — Boltzmann, Ising Model, Phase Transitions and the Arrow of Time
Maxwell-Boltzmann, Lennard-Jones molecular dynamics, Ising model critical point, blackbody radiation, Carnot cycle and Brownian diffusion — statistical physics from first principles.
Quantum Mechanics & Wave Functions — Schrödinger, Tunnelling, Double-Slit and Quantum Circuits
Schrödinger equation, quantum tunnelling, hydrogen orbitals, qubit gates and Grover's algorithm — quantum physics through interactive simulation.
Differential Equations in Biology — Lotka-Volterra, Hodgkin-Huxley and Enzyme Kinetics
How ODEs power biological modelling: population cycles, neuron spikes, enzyme saturation kinetics, and epidemic thresholds.
Probability & Statistical Inference — Bayesian Reasoning, CLT and Markov Chains
Bayes' theorem, central limit theorem, Markov chains, OLS regression, Monte Carlo and bootstrap resampling — 7 interactive sims.
Signal Processing & Fourier — FFT, Digital Filters, AM/FM and Doppler
Fourier series, Cooley-Tukey FFT, FIR/IIR filters, OFDM, RLC resonance and the Doppler effect — 8 interactive sims.
Graph Theory & Algorithms — Dijkstra, A*, MST and Force-Directed Layouts
Dijkstra, A* search, Kruskal MST, TSP, force-directed graphs, maze generation and decision trees — 7 interactive sims.
Optics & Ray Tracing — Snell's Law, SDF Ray Marching & Fresnel
From Snell's law and Fresnel equations to SDF sphere tracing and Rayleigh scattering — six interactive optics simulations with the physics of light explained.
Statistical Mechanics — Boltzmann, Ising Model & Metropolis
Microstates to macrostates: Maxwell-Boltzmann distributions, Ising ferromagnets, Monte Carlo sampling, and phase transitions — with the Metropolis algorithm in full detail.
Waves & Fourier Analysis — DFT, FFT & Signal Processing
From wave superposition to Cooley-Tukey FFT — why the DFT works, Nyquist sampling, the z-transform, and interactive sims from standing waves to Chladni figures.
Machine Learning — Backprop, SGD, Adam & Neural Networks
Gradient descent maths, backpropagation chain rule with code, SGD vs momentum vs Adam, CNNs, reinforcement learning, genetic algorithms, and interactive sims to try them all.
Complexity & Emergence — Chaos, Attractors & Self-Organisation
Lorenz equations, bifurcation diagrams, Lyapunov exponents, fractal dimension, and self-organised criticality — the deep maths of complex systems.
Differential Equations — Euler, RK4, Verlet & Finite Differences
Four numerical integration methods compared with code — why RK4 beats Euler, when to use Verlet, and how finite differences solve PDEs on a grid.
GLSL Shaders from Zero — Graphics for Non-GPU Programmers
Fragment shaders, SDF circles, value noise, and the whole Three.js ShaderMaterial pipeline — no prior GPU experience needed.
Monte Carlo Methods — Randomness as a Computational Tool
Estimating π by throwing darts, integrating impossible integrals, and every site simulation that secretly runs a Monte Carlo loop.
Cellular Automata — From Game of Life to Forest Fires
How a grid of cells with two states and four rules can produce self-replication, Turing completeness, and snowflake patterns.
Agent-Based Models — From Ants to Financial Markets
Why thousands of simple agents following local rules produce complex global behaviour — boids, ant trails, epidemics, bank runs.
Numerical Methods — Euler, RK4 & Verlet in Simulations
Why the simple Euler method explodes, why RK4 is the workhorse, and why Verlet conserves energy in physics engines.
WebGL for the Complete Beginner — No GPU Experience Needed
What WebGL actually is, why it matters for physics simulations, and how the CPU-to-GPU pipeline works — explained without jargon.
💡 Tips & Tricks
Responsive Canvas & HiDPI — ResizeObserver, devicePixelRatio and Pointer Events
Crisp WebGL on retina displays, container-aware resize, unified pointer/touch events, and CSS contain:strict for layout perf.
Three.js Memory Management — dispose(), WebGL Context Limits and Leak Detection
Geometry, material and texture dispose() patterns, WebGL context cap, renderer.info leak detection, WeakRef pooling.
Physics Timestep Patterns — Fixed dt, Sub-stepping & Deterministic Replay
Fixed timestep accumulator, sub-stepping for stiff constraints, render interpolation, spiral-of-death prevention, and deterministic replay — with copy-paste JavaScript.
GLSL Procedural Noise — Perlin, Worley, FBm & Domain Warping
Value noise, gradient (Perlin) noise, Worley cell noise, fractional Brownian motion, and domain warping — all with copy-paste GLSL code and live demos.
TypeScript + Three.js Without a Build Step
Import maps, @types/three, JSDoc @ts-check — get full IntelliSense and type safety on CDN Three.js. Five common type pitfalls and how to fix every one.
Three.js r160 — WebGPU Renderer Beta & Migration Guide
WebGPU renderer + TSL NodeMaterial are now beta. New dispersion and iridescence on MeshPhysicalMaterial, breaking GLTFLoader changes, and a migration checklist.
Web Workers for Heavy Physics — Keep the Main Thread Free
Move your physics loop off the render thread: transferable ArrayBuffers, SharedArrayBuffer + Atomics, and when workers actually hurt rather than help.
Schema.org JSON-LD for Simulation Sites
Four Schema types that boosted this site's CTR from 2.1% to 4.8%: SoftwareApplication, BreadcrumbList, FAQPage, and CollectionPage — with complete copy-paste examples.
8 Techniques for 60 FPS Canvas 2D Physics
Typed arrays, batched paths, ImageData tricks, fixed timestep, OffscreenCanvas, spatial hashing — the exact techniques that make Canvas 2D physics run at 60 FPS even on mobile.
Accessibility for Interactive Simulations — ARIA, Keyboard, Reduced Motion
ARIA live regions, keyboard-first controls, prefers-reduced-motion, WebGL colour contrast, and a 12-point compliance checklist.
WebAssembly for Browser Physics Engines — When WASM Actually Helps
Rust-to-WASM compilation, zero-copy SharedArrayBuffer patterns, real benchmarks (6× speedup on cloth), and when WASM adds complexity without benefit.
Canvas 2D vs Three.js — The Right Tool for Each Sim
An 11-row comparison table and decision checklist — when to reach for a 2D canvas and when you actually need WebGL. Based on building 225 simulations with both.
InstancedMesh Changed Everything — 5 FPS to 60 FPS
Rendering thousands of identical objects is the most common Three.js performance trap. One API call — InstancedMesh — solves it completely. Benchmarks and code included.
How I Debug GLSL Shaders (and Keep My Sanity)
No console.log in GLSL. No breakpoints. Just a black screen. Here are my practical tools and workflow for debugging vertex and fragment shaders — including the colour-as-value trick.
Disposing Three.js Objects Correctly (No Memory Leaks)
Geometry, material, texture and renderer — all leak if you don't call dispose() correctly. The complete checklist I use before every simulation cleanup.
Cannon-es vs Rapier.js — Choosing a Browser Physics Engine
Both run in the browser; both handle rigid bodies. So which do you pick? A practical side-by-side comparison based on building simulations with each.
Three.js vs Babylon.js — Which WebGL Framework?
Two mature WebGL frameworks, very different philosophies. I built the same simulation in both and here's what I found: bundle size, API ergonomics, shader access and ecosystem differences.
requestAnimationFrame vs setInterval — Always Use rAF
setInterval can't match the display refresh rate, wastes CPU in hidden tabs, and causes jitter. Here's exactly why rAF wins for animations and simulations, plus the fixed-timestep pattern that prevents physics explosions.
Useful Three.js Snippets I Use Every Day
8 copy-paste code blocks I reach for in every project: pixel-ratio renderer setup, resize handler, texture loader with callbacks, instanced matrix update, BufferGeometry from typed arrays, and more.
CSS Grid for Responsive Simulation Cards
auto-fill vs auto-fit, minmax() columns that work from 320 px to 4 K — no media queries needed. The exact grid setup behind this site's simulation catalogue, with a live editable demo.
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