00 · the lab
Generative experiments
Small canvas animations spanning generative art, mathematics, and physics — each with live knobs and a note on how it works. Tune them, share a link, steal the idea.
Guides
Concept guides
Friendly walkthroughs that build from a live simulation into the underlying idea.
Complex Maps and Airfoils
∫ MathematicsThe Joukowski transform turning circles into airfoils, with conformal geometry as the translator.
- complex analysis
- conformal mapping
- aerodynamics
Sensitive Dependence
∫ MathematicsWhy deterministic systems can still become practically unpredictable when nearby states peel apart.
- chaos
- prediction
- lyapunov
Turing Patterns
∫ MathematicsLocal reaction plus uneven diffusion can draw stripes, spots, and labyrinths without a central planner.
- reaction diffusion
- turing
- pattern formation
Aliasing and Nyquist
Ω Electrical EngineeringWhat happens when a sampled signal masquerades as a slower wave because the clock was too lazy.
- dsp
- sampling
- nyquist
Feedback Stability Margins
Ω Electrical EngineeringA Bode-plot view of how much phase and gain slack a feedback loop has before it rings or runs away.
- control
- bode
- stability
◆·Generative Art
Canvas animations exploring noise, flow, and organic form.
Orbits
◆ Generative ArtBodies tracing a shared circle, leaving light trails.
- trails
- trig
Flow Field
◆ Generative ArtParticles advected by a value-noise vector field.
- noise
- particles
Starfield
◆ Generative ArtParallax warp toward a vanishing point.
- 3d
- parallax
Cyclic Automaton
◆ Generative ArtCells advancing in a colour cycle when enough neighbours lead.
- automata
- grid
Ripple Grid
◆ Generative ArtA dot grid pulsing with summed sine-wave interference.
- waves
- grid
Mesh Wave
◆ Generative ArtIsometric wireframe terrain with layered sine waves.
- 3d
- wireframe
Voronoi Bloom
◆ Generative ArtDrifting gradient blobs blending into organic stained-glass cells.
- voronoi
- gradient
Flow Streams
◆ Generative ArtInk-like streamlines curling through a noise field.
- noise
- ink
Metaball Bloom
◆ Generative ArtOrganic gradient blobs merging and splitting in lava-lamp motion.
- gradient
- organic
Spirograph Rose
◆ Generative ArtLayered parametric curves drawing vintage generative spirographs.
- parametric
- curves
Dot Lattice
◆ Generative ArtA breathing dot grid modulated by layered noise waves.
- grid
- noise
Boids Flocking
◆ Generative ArtSeparation, alignment, and cohesion steering leaderless agents into murmuration-like flocks.
- boids
- flocking
- emergence
- swarm
Truchet Tiles
◆ Generative ArtA grid of coin-flip tiles whose arcs join into one continuous, slowly reseeding labyrinth.
- tiling
- generative
- grid
- labyrinth
∫·Mathematics
Visualising differential equations, geometry, and statistics.
Double Pendulum
∫ MathematicsChaotic pendulums diverging from near-identical starting conditions.
- chaos
- ode
Logistic Bifurcation
∫ MathematicsThe period-doubling cascade of x → r·x·(1−x): fixed point, 2-cycle, 4-cycle, then chaos, with a live cobweb inset.
- chaos
- bifurcation
- dynamical systems
Phase Portrait
∫ MathematicsODE trajectories flowing through vector fields — Lotka-Volterra, Van der Pol, Duffing.
- ode
- dynamical systems
Conformal Grid
∫ MathematicsComplex mappings deforming a Cartesian grid — Joukowski, power maps, inversion.
- complex analysis
- differential geometry
Random Walk
∫ MathematicsStochastic walks converging to the Gaussian via the central limit theorem.
- statistics
- probability
Fourier Series
∫ MathematicsEpicycles tracing waveforms — Gibbs phenomenon, harmonic decomposition.
- analysis
- fourier
Lorenz Attractor
∫ MathematicsThe classic chaotic 3D butterfly — two trajectories diverge from near-identical starts.
- chaos
- ode
- butterfly effect
Reaction-Diffusion
∫ MathematicsGray-Scott Turing patterns — spots, stripes, mazes, and mitosis from two PDEs.
- pde
- turing
- pattern formation
Mandelbrot & Julia
∫ MathematicsEscape-time fractals of z² + c — a morphing Julia set and the Mandelbrot atlas, smooth-coloured through a brand palette.
- fractals
- complex dynamics
- escape-time
ψ·Physics
Waves, quantum states, and condensed-matter phenomena.
Wave Superposition
ψ PhysicsInterference of two plane waves — beats, standing waves, and nodes.
- waves
- interference
Bloch Sphere
ψ PhysicsQubit state precessing on the Bloch sphere under a magnetic Hamiltonian.
- quantum
- qm
Band Structure
ψ PhysicsNearly-free electron E-k diagram with Brillouin zone gaps.
- condensed matter
- solid state
Quantum Tunneling
ψ PhysicsGaussian wave packet tunnelling through a rectangular barrier.
- quantum
- tunneling
Coupled Oscillators
ψ PhysicsTwo mass-spring systems exchanging energy via normal-mode beating.
- mechanics
- normal modes
- beats
Ising Model
ψ PhysicsMagnetic spins ordering into domains below the critical temperature and melting into noise above it.
- statistical mechanics
- monte carlo
- phase transition
- magnetism
Kinetic Theory of Gases
ψ PhysicsHard discs colliding in a box relax into the 2D Maxwell-Boltzmann speed distribution.
- thermodynamics
- statistical mechanics
- collisions
- maxwell-boltzmann
Ω·Electrical Engineering
Circuits, signal processing, control systems, and software radio.
RLC Resonance
Ω Electrical EngineeringTransient step response of a series RLC circuit — underdamped ringing vs critical damping.
- circuits
- transient
FFT Spectrum
Ω Electrical EngineeringReal-time frequency analyzer with log-scale bins — sine, square, sawtooth, chirp waveforms.
- dsp
- spectrum
PID Tuner
Ω Electrical EngineeringStep response of a PID-controlled 2nd-order plant — tune Kp, Ki, Kd and watch overshoot and settle.
- control
- feedback
Constellation Plot
Ω Electrical EngineeringQPSK / 16-QAM / 64-QAM scatter through an AWGN channel — adjustable SNR and EVM.
- communications
- modulation
Smith Chart
Ω Electrical EngineeringTransmission line impedance matcher — animated reflection coefficient path as frequency sweeps.
- rf
- impedance
Inverse Kinematics
Ω Electrical Engineering2R planar robot arm solving for joint angles via analytic IK — drag the end-effector.
- robotics
- kinematics
PLL Lock-In
Ω Electrical EngineeringPhase-locked loop tracking a chirped reference — P/PI loop filter, VCO frequency, lock-in visualisation.
- control
- pll
Bode Plotter
Ω Electrical EngineeringFrequency response of 1st–4th order filters — LP/HP/BP/Notch with animated pole movement.
- dsp
- filters
Transmission Line Pulse
Ω Electrical EngineeringTDR — a voltage pulse travels, reflects, and inverts on a mismatched line.
- rf
- tdr
- impedance
AM Modulation
Ω Electrical EngineeringCarrier, message, modulated signal, and spectrum — envelope, sidebands, overmodulation.
- communications
- modulation
- rf
Pole-Zero Explorer
Ω Electrical EngineeringA conjugate pole pair on the s-plane, live-mapped to step response and Bode magnitude.
- control
- s-plane
- poles
- bode
Eye Diagram
Ω Electrical EngineeringOverlaid symbol traces forming a digital-comms eye — SNR, bandwidth, and roll-off open or close the decision margin.
- communications
- dsp
- signal integrity
Circuit Simulator
Ω Electrical EngineeringDrag-and-drop circuit builder with SPICE-style transient simulation and a built-in oscilloscope.
- circuits
- spice
- mna
- oscilloscope
✦·AI & Machine Learning
Attention, transformers, and the mechanics of deep models.
Self-Attention
✦ AI & Machine LearningMulti-head self-attention as a live particle network — query tokens cycle, heads drift, weights flow.
- attention
- transformer
- deep-learning
- neural networks
Gradient Descent
✦ AI & Machine LearningSGD, Momentum, RMSProp, and Adam racing down a loss landscape — ravines, saddles, and local minima.
- optimization
- deep-learning
- training
A* Pathfinder
✦ AI & Machine LearningA*, Dijkstra, and greedy best-first search — the heuristic pulling the frontier toward the goal.
- search
- graphs
- a-star
k-Means Clustering
✦ AI & Machine LearningLloyd's algorithm on Gaussian blobs — points snap to their nearest centroid, then centroids glide to each mean.
- clustering
- unsupervised
- lloyd
- voronoi
Neural Decision Boundary
✦ AI & Machine LearningA tiny MLP trained live, its decision boundary bending to separate spirals, moons, circles, and XOR.
- neural networks
- backpropagation
- classification
- decision boundary
✷·Cosmology
Spacetime, black holes, and the structure of the universe — from the Planck length to the cosmic web.
Universe Scale
✷ CosmologyA logarithmic zoom from the Planck length to the observable universe — ant, whale, Everest, Earth, Sun, galaxy.
- scale
- cosmology
- powers of ten
- log
Spacetime Curvature
✷ CosmologyA mass curving an embedding sheet, with geodesics and bending light rays.
- general relativity
- geodesics
- gravity
Black Hole
✷ CosmologySchwarzschild geometry: event horizon, photon sphere, ISCO, lensing shadow, and an infalling probe.
- black hole
- schwarzschild
- event horizon
Black Hole Ray Tracer
✷ CosmologyA general-relativistic ray tracer: per-pixel null geodesics around a Schwarzschild black hole, with a physically-shaded accretion disk, Doppler beaming, and live EHT-scale readouts.
- general relativity
- ray tracing
- geodesics
- accretion disk
- webgl
Holographic Bound
✷ CosmologyEntropy scales with area, not volume — pixels tiling a horizon, and the Bekenstein bound.
- holographic principle
- entropy
- bekenstein bound
Cosmic Expansion
✷ CosmologyThe FLRW scale factor a(t), Hubble flow, redshift, and the fate of the universe.
- cosmology
- flrw
- hubble
- dark energy
CMB Sky
✷ CosmologyThe last-scattering temperature map and its acoustic-peak power spectrum.
- cmb
- cosmology
- acoustic peaks
Galaxy Rotation Curve
✷ CosmologyKeplerian decline vs the observed flat curve, and the dark-matter halo that flattens it.
- dark matter
- galaxy
- rotation curve
HR Diagram
✷ CosmologyA star's evolutionary track across the Hertzsprung-Russell diagram, by initial mass.
- stars
- stellar evolution
- hr diagram
Gravitational-Wave Chirp
✷ CosmologyA compact-binary inspiral strain h(t): chirp, merger, and ringdown, with a spectrogram.
- gravitational waves
- ligo
- inspiral
Fine-Tuning Dials
✷ CosmologyNudge the constants of nature and watch a habitability readout collapse off-tune.
- anthropic
- fine-tuning
- multiverse
Gravitational Lensing
✷ CosmologyA foreground mass bends background light into twin arcs and a full Einstein ring.
- general relativity
- lensing
- einstein ring
Exoplanet Transit
✷ CosmologyA planet crossing a limb-darkened star, drawing its dip in the measured light curve.
- exoplanets
- photometry
- transit