Educational Centre

Maths and physics behind simulations — from SPH hydrodynamics to Lorenz chaos and GLSL shaders. Read, learn, build.

50+Articles
15Tutorials
8References

💧 Particle Physics

3 articles
ArticlePhysics
SPH — Smoothed-Particle Hydrodynamics
Poly6, Spiky, Viscosity kernels. Pressure, viscosity, boundary conditions. Browser implementation.
SPHFluid
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ArticleAstrophysics
N-Body and the Barnes-Hut Algorithm
Leapfrog integrator, O(N²) vs O(N log N). Octree for scaling to 100k bodies.
N-bodyOctober
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ArticleMathematics
Verlet, Leapfrog and RK4 — Numerical Integration
Comparison of ODE integration methods: stability, accuracy, computational cost.
VerletRK4
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🌊 Waves & Fluids

4 articles
ArticleGLSL
Gerstner Waves in GLSL
Trochoidal waves, Fresnel effect, foam. Maths and vertex shader code.
GLSLOcean
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ArticleMathematics
Wave Equation in 2D and 3D
Partial differential equations, finite differences, standing waves.
PDEWave
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ArticlePhysics
Lattice Boltzmann Method (LBM)
CFD via statistics. D2Q9 model, BGK collision equation, turbulence in the browser.
LBMCFD
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ArticlePhysics
Navier-Stokes Equations in WebGL
Advection–diffusion–projection (Jos Stam "Stable Fluids"), projected-gradient solver.
Navier-StokesWebGL
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🐦 Agent Algorithms

4 articles
ArticleSwarm Intelligence
Boids Algorithm — Reynolds' Three Rules
Separation, alignment, cohesion. Pseudocode, spatial partitioning, InstancedMesh.
BoidsSwarm
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ArticleAlgorithms
ACO — Ant Colony Optimisation
Pheromone trails, stigmergy, shortest-path finding. Canvas 2D implementation.
ACOOptimization
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ArticleModelling
SIR/SEIR Epidemic Spread Model
Differential equations of population biology. R₀, herd immunity threshold.
SIRBiology
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ArticleMathematics
L-Systems and Plant Growth
Lindenmayer grammars, Turtle graphics, recursive trees, Barnsley fern.
L-systemsFractal
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🌀 Chaos & Dynamic Systems

2 articles
ArticleChaos
Lorenz Attractor and the Butterfly Effect
Lorenz 1963 ODE system, sensitivity to initial conditions, strange attractor in 3D.
ChaosODE
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ArticleChaos
Double Pendulum and Runge-Kutta Method
Lagrange equations, RK4 numerical integration, Lyapunov chaos exponent.
RK4Pendulum
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🧬 Cellular Automata

2 articles
ArticleCellular Automata
Conway's Game of Life — Maths and Patterns
B3/S23 rules, Gosper glider gun, pulsar, HighLife. Complexity from simplicity.
ConwayCA
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ArticleChemistry
Reaction-Diffusion and Turing Patterns
Gray-Scott system, F and k parameters, zebra stripes, tiger spots — morphogenesis in JavaScript.
Gray-ScottTuring
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🔭 Astrophysics

2 articles
ArticleAstronomy
Planetary Orbits and Kepler's Laws
Kepler's three laws, gravitational parameter μ, Kepler's equation. Three.js implementation.
KeplerOrbits
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ArticleAstrophysics
Spiral Arms of Galaxies
Density wave theory, logarithmic spiral, procedural generation of 80k stars.
GalaxyParticles
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📐 Mathematics

3 articles
ArticleProcedural Generation
Perlin Noise and fBm
Gradient noise, octaves, fractional Brownian motion. Terrains, clouds, textures.
PerlinNoise
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ArticleGeometry
Voronoi Diagrams
Fortune's algorithm, Delaunay triangulation, applications in physics and terrain generation.
VoronoiGeometry
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ArticleFractals
Fractal Geometry and Dimension
Mandelbrot set, Hausdorff fractal dimension, IFS iterated function systems.
MandelbrotFractal
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💻 Computer Graphics

3 articles
ArticleRendering
Ray Tracing from Scratch
Rays, sphere/triangle intersection, shadows, reflections, BVH acceleration.
Ray TracingBVH
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ArticleGLSL
Ray Marching and SDF
Signed Distance Functions, sphere-tracing, ambient occlusion, soft shadows in GLSL.
SDFGLSL
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ArticleShaders
Procedural Textures in GLSL
FBM, Worley noise, marble, wood, reptile skin. All using maths in the shader.
GLSLProcedural
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🎓 Tutorials

11 tutorials
01
Your First Simulation in 30 Minutes
Three.js from scratch: renderer, scene, camera. Five steps to moving particles.
⏱ 30 minBeginner
02
Three.js for Beginners
Geometries, materials, lighting, textures, OrbitControls — all the basics.
⏱ 45 minBeginner
03
GLSL Shaders from Scratch
Vertex and fragment shaders, uniforms, varyings, passing data to the GPU.
⏱ 60 minIntermediate
04
Cannon-es: Physics Bodies and Collisions
World, Body, Shape. Syncing Three.js + Cannon-es. RaycastVehicle.
⏱ 50 minIntermediate
05
Optimising Simulations: InstancedMesh and Spatial Hashing
From 500 to 50,000 particles at 60fps. InstancedMesh, WebWorker, spatial hashing.
⏱ 40 minAdvanced
06
Fluid Simulation in an Evening
SPH implementation from scratch. Spatial partitioning, kernels, integration. Full code.
⏱ 90 minAdvanced
07
How to Build Your Own Simulation
Template from idea to publication. File structure, HUD, controls hint, responsive.
⏱ 35 minBeginner
08
Pathfinding Algorithm Visualiser
A*, Dijkstra, BFS in live animation on Canvas 2D. Maze + interactive walls.
⏱ 70 minIntermediate
09
Solar System in Three.js
Textured planets, Keplerian orbits, CSS2D labels, speed slider, UnrealBloom post-processing.
⏱ 60 minIntermediate
10
GLSL Fire & Water Shader
fBm noise fire with colour ramp, Gerstner waves, Fresnel caustics — raw WebGL2 & Three.js ShaderMaterial.
⏱ 55 minAdvanced
11
Save Settings with localStorage
Persist slider values, toggles and camera state across reloads with JSON, schema versioning and IndexedDB.
⏱ 35 minBeginner

📚 References

8 references
🔧
WebGL Cheatsheet
API, states, extensions
 ✨
GLSL Cheatsheet
Functions, types, precisions
 📐
Mathematical Formulae
Vectors, matrices, quaternions
 ⚛️
Physical Constants
G, c, kB, h, NA
 📖
Algorithm Glossary
SPH, BVH, ACO, RK4…
 🔢
Numerical Methods
ODE integration, PDE
 📊
Algorithm Complexity
Big-O table for simulations
 ⚖️
Simulation Comparison
Cost, accuracy, approach
🔍

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