Simulations
Interactive, browser-native physics — every simulation a single file, no installs, no network (bar the one page of live satellite data), opened straight off the disk. Sixty-seven of them, grouped by subject; click a card to launch it.
Mechanics & Control
Cart & Pendulum
Swing-up on a rail: pump energy through the pivot, go over the top, and hand off to an LQR balance controller — Riccati solved in-page, one or two links.
Lagrangian Mechanics
A block on a fixed wedge done by the calculus of variations: one coordinate that respects the constraint, the normal force recovered as a Lagrange multiplier, and the angle of repose where friction holds.
PID Controller
A control loop drawn from its exact algebra — block diagram, transfer functions, the root locus wandering the s-plane as you turn the gains, and the step response beside it. Feedback moves poles, never zeros.
Why Three, and Only Three
Three-phase power and the three-bladed wind turbine are the same root-of-unity theorem: quadratic quantities turn isotropic at N = 3, so the machine stops shaking. The same sum, evaluated twice.
Brachistochrone
Bernoulli's 1696 challenge raced live: six beads between the same two points, the cycloid first every time and your own curve never. Snell's law bends a light ray onto it, beads dropped anywhere on the bowl arrive together, Huygens' cycloidal cheeks keep exact time, and every descent is a quadrature pinned to scipy.
Waves & Optics
Diffraction
Slits, gratings and circular apertures by three routes — Fraunhofer closed forms, Fresnel's near field on the Cornu spiral, and the raw Rayleigh–Sommerfeld integral — all live at once so they can be watched disagreeing.
Lenses
Rays traced the hard way — Snell's law in vector form at every surface, nothing paraxial anywhere — so the lens maker's equation is checked against the trace in the limit rather than used by it.
Refraction
One law does the geometry, the Fresnel pair does the energy: Snell, Brewster's fully-polarized bounce, and past the critical angle the trapdoor of total internal reflection — drawn as rays and as real wavefronts.
Drum Head
The wave equation on a disc, separated into Bessel functions — and the rim does the quantising: clamped, free or springy edges each reshape the spectrum. Struck, radiating, and resonant — and now audible, in real time or slowed four hundred times.
Fourier
The transform as a winding machine, the series as epicycles closing in on a square wave — Gibbs overshoot and all — and the FFT's even/odd split drawn butterfly by butterfly.
Wave Fronts
One wave has one speed, a packet has two: phase and group velocity measured live on a finite superposition, quantum mechanics' factor of two raced against Newton, Apollonius on the dispersion parabola, and deep-water waves as the classical mirror image — crests dying at the front of their own group.
Electromagnetism
Dipole Radiation
Exact retarded fields of point multipoles: antenna stacks climbing the ladder from dipole to 16-pole, field lines pinching off each half cycle, and a rotating dipole winding the pulsar pinwheel inside its light cylinder.
Radio Waves
A broadcast antenna driving a little radio — message, modulator, antenna current, retarded fields, receiver, demodulator — with the AM tower's ground image and the FM mast's elevation lobes computed exactly.
Waveguides
TE, TM, TEM and hybrid modes in six guide shapes. Each cross-section sets one cutoff eigenvalue; one dispersion relation does the rest — below cutoff the pipe becomes a filter that dissipates nothing.
Signals & Sound
Oscilloscope
A two-channel function generator into a digital storage scope: exact Fourier-series waveforms through an honest LTI signal path — source loading, probes, the scope's own input — one complex transfer function per harmonic.
RLC Band-Pass Filters
Every way to arrange one R, one L and one C, and the two that pass a band; the series and the parallel resonator with their phasors, magnification and a lossy coil’s four centre frequencies; Butterworth, Chebyshev and Bessel ladders; two coupled tanks; the poles behind them all; and a radio dial you can hear, tuned from station to station through the static between them.
Voltage & Current Dividers
Resistors in series split a voltage and resistors in parallel split a current: the two dividers side by side, the circuit as a landscape of potential, a divider under load with its Thévenin equivalent, an analog multimeter built from one movement, Wheatstone, strain-gauge and thermistor bridges, and the R–2R and Kelvin–Varley ladders.
Fluids & Flight
Buoyancy
Archimedes’ principle from the spring scale to the metacentre: the upthrust read off a beaker and built from the pressure on every face, what floats and how deep, why a square log rolls onto its corner, whether the crown was gold, and why a Cartesian diver can never hover.
Turbojet
Ramjet, turbojet, turbofan and turboprop as one machine with two knobs — asserted as exact limits of each other — and a Brayton loop that closes through the sky: its area is the kinetic energy handed to the air.
Wind Tunnel
A working wind tunnel, not a picture of one: a lattice-Boltzmann Navier–Stokes solver running in the page, its viscosity identity measured by decaying a shear wave rather than quoted.
Heat & Thermodynamics
Power Cycles
Eight cycles as closed loops on their real state surfaces — Carnot & Rankine on IAPWS steam, Otto through Stirling on variable-cp air; P–v and T–s are the two shadows.
Blackbody Radiation
Planck's curve in true SI — σ, Wien's b and ζ(3) derived at boot — with Rayleigh–Jeans leaving the top of the plot, an exactly-sampled photon gas, and every temperature drawn in its honest glow color.
Quantum Mechanics
Hydrogen Orbitals
The hydrogen atom's electron clouds as rotatable Monte-Carlo point clouds — exact ψnlm sampling, real or complex orbitals, with the closed-form wavefunction printed live.
Particles in a Box
One and two particles in the infinite well under exact spectral evolution: revivals to machine precision, bosons bunching on the diagonal, and the fermion exchange hole — an exact zero along x1 = x2.
Quantum Tunneling
A Gaussian packet meeting one or two barriers under unitary Crank–Nicolson, absorbing boundaries book-kept into live T and R — and with two barriers, the resonances where transmission touches one.
Harmonic Oscillator
The oscillator both ways: a classical ball in the bowl beside the exact Hermite-basis quantum evolution — eigenstates, beating superpositions, and the coherent state that follows the ball forever without spreading.
Rabi Oscillations & Superoscillations
A driven atom flops between two levels: on the Bloch sphere in the lab and in the frame turning with the drive, with the Bloch–Siegert shift, π pulses and Ramsey’s fringes, decay and the Mollow triplet, and the collapse and revival in a quantized field. Then a post-selected turn that runs faster than it can: the weak value, Berry’s superoscillations, and a focus narrower than the diffraction limit.
Atoms, Matter & Light
Periodic Table
Why the table has the shape it has: Moseley's integer Z, block widths 2(2l+1), the Madelung rule constructed for all 118 elements — and every place nature disagrees with it, marked.
Hyperfine Structure
The nucleus splits every level of the atom: Steck’s rubidium-85 diagrams recomputed from his constants and drawn the same way for hydrogen through chromium, krypton and the KrF excimer, the spectrum a warm gas absorbs, every sublevel in a magnetic field out to Paschen–Back, the transitions light drives between them, and J and I turning together as F.
Crystal Lattices
BCC, FCC and HCP as exact hard-sphere packings — stacking orders, packing fractions, and cell clipping in a hand-rolled 3-D renderer.
p–n Junctions & Transistors
Silicon from the dopant up: donors that freeze out and ionize, a junction’s field solved exactly against the depletion approximation, a whole diode by drift-diffusion (and lit, a solar cell), electrons random-walking across a bipolar base, a MOSFET’s inversion layer, and the amplifier and CMOS inverter they make. Then the bands of a blue LED, built one layer at a time: the Fermi levels meeting, the InGaN wells filling and glowing under forward bias.
Lasers
Six machines, one mechanism — ruby, He–Ne, diode, Rigrod's cavity algebra, dye, NIF — each panel integrating its own rate equations live, from Maiman's relaxation spikes to ignition.
Excimer Lasers
KrF and ArF: the lower level destroys itself in a picosecond, so the excimer must be assembled collision by collision — ion and harpoon channels animated, every rate constant lifted from my own plasma-kinetics research codes.
Nuclear Clocks
Five references across eleven decades, caesium to the 229Th nuclear isomer: the locked loop every clock is, Ramsey fringes buying line quality, and the Allan-deviation ladder down to quantum noise.
The Standard Model from Symmetry
SU(3) × SU(2) × U(1) taken apart: one boson per generator, a generation of fermions whose charges the anomalies fix, the Higgs potential and the masses it hands out, the eightfold way’s octets and decuplets with measured masses, colour singlets, and three couplings that almost meet.
Amino Acids in 3-D
The twenty building blocks of proteins as turning molecules: why they are all left-handed (and why L-cysteine is still called R), the helices a chain of them winds into, the few backbone angles that do not collide, and the code that spells them.
Scattering & Brillouin Physics
Differential Scattering
What a cross section is: the Jacobian from impact parameter to solid angle, Coulomb hyperbolas past a nucleus drawn at true radius, Geiger & Marsden's 1913 rows, and the form-factor dip that sizes a nucleus.
Light Scattering
The classic triad from one pump: Raman lines that ignore the scattering angle, the Brillouin doublet that moves with it, and the Landau–Placzek ratio tying the central line to γ − 1 — five decades on one screen. Then Brillouin as Bragg reflection off a moving sound wave, and two cousins from the sky: sun dogs refracted by falling ice plates, and the glory’s coloured rings around your own shadow, which measure the droplets.
SERS & TERS
Raman scattering made a million times brighter by a metal’s plasmon, two ways: a rough silver film where one gap in 24 does 60% of the shining (Fang, Seong & Dlott’s measured hot-spot law) until a two-nanometre spacer kills it, then a gold tip’s single hot spot, the |E|⁴ law that wants the pump and the Stokes line both on the plasmon, and anti-Stokes light that needs heat.
Blue Sky
Why the sky is blue, and why twilight stays blue: Rayleigh’s ω⁴ along every line of sight with the planet’s shadow cut out of it, ozone’s Chappuis band, and the sun from noon to straight underfoot, on twelve worlds — Earth (with and without ozone), Mars, Venus, Titan, the Moon, Mercury, Jupiter, Saturn under its rings, Uranus, Neptune and Pluto — in lux and cd/m² against what was measured, and, over the sea, the green flash.
Astrophysics & Relativity
Solar-System Ephemerides
Planets and moons from JPL mean elements, a relativistic upgrade, and an intrinsic Weyl-scalar chart — three reference frames side by side, LISA riding along.
Lagrange Points
The five balance points of two orbiting bodies: where they are and which are stable, the halos SOHO and JWST fly about L1 and L2, the Lunar Gateway’s near-rectilinear orbit, and Jupiter’s trojans librating on the hilltops of the effective potential.
The Hohmann Transfer
Periapsis and apoapsis round five bodies, the two-burn ellipse between circular orbits and why its burns go at the apsides, one burn anywhere (the Oberth effect), the cost against the bi-elliptic route, the launch windows to the planets against every Mars launch since 1960, and the apse line turned by the Earth’s bulge and by relativity.
Earth Observation, Live
Today’s planet as NASA, NOAA, EUMETSAT, JMA and Copernicus satellites see it, fetched live — LANCE mosaics, five geostationary disks, a day of fires, Sentinel scenes — each set against the page’s own orbits, swaths, Planck’s law and fixed grid. The one page here that needs the network.
The Earth’s Interior
The Earth cut open to scale on PREM’s layers, the solid mantle creeping in a convection model that runs as you watch, Bird’s 52 plates turning about their Euler poles, the iron core’s field from IGRF-14 at the surface and continued down to the core, and the seismic rays whose shadow found the liquid core and whose faint arrivals found the solid one inside it.
The Sun
The Sun cut open on Model S, its core’s burning computed from the nuclear rates and its neutrinos set beside the experiments, HMI’s sound waves on the ridges Duvall’s law makes of them, the sunspot cycle and the polar fields a flux transport model rebuilds, and a coronal mass ejection followed from the corona, through a synthetic LASCO image, out to the Earth.
Solar Winds
One coronal mass ejection from start to finish: an arcade of closed loops pinches off round a flux rope that loses its equilibrium and erupts, the cloud crosses to the Earth behind its own shock, opens the Earth’s field and comes down as the aurora — the oval over the pole, and the curtain as a city sees it, coloured by the height each line is made at.
Red Sprites
A positive stroke drains a storm’s charge and its field soaks up through the atmosphere, a leaky dielectric over a conducting ground, faster than the air aloft can screen it; where it beats the breakdown field near 75 km a sprite of streamers grows down and up, red above and blue below from the quenching of nitrogen’s bands — in cross-section, from a camera on the ground through the reddening air, and from orbit against the limb, with the elve racing out at 90 km.
Lightning
The kinds of lightning NSSL lists, grown rather than drawn: a storm’s charges and the field they make against the two breakdown thresholds, a leader grown cell by cell in that field until it strikes the ground, a tower, a tree or a house, or stays in the cloud as a sheet, or runs out into the air — negative and positive, upward from a tower, the bolt from the blue, spider lightning — with its return strokes, dart leaders and continuing current; the storm from far away, where the Earth’s curve and the bending of sound make heat lightning; and the blue and gigantic jets above, coloured by the same quenching as the sprites.
Granulation
A 3-Mm patch of the Sun’s surface computed live on the GPU: the gas ionising, its opacity from the cross-sections, the light it loses and the field it carries; hot gas rises in granules, radiates, and sinks in the lanes, sweeping the field into kilogauss sheets that depress the surface — and seen from 32°, as the Inouye telescope saw it, the granules’ walls show the striations, dark where the sheet’s field is weaker and the surface stands higher.
Pulsar
A rotating magnetised neutron star six ways: the beam sweeping a line of sight, the polarisation swing that measures the geometry, 23 real pulsars on the spin-down diagram, and the binary that weighed general relativity.
Binary Merger
Two black holes' last second: the post-Newtonian chirp, the Kerr ringdown from fits to the Teukolsky spectrum, and between them an honestly-dashed stitch where only numerical relativity truly knows.
Standard Candle
The Chandrasekhar equation of state integrated in the page, the mass–radius relation that simply ends, 143 measured white dwarfs, 29 real light curves — and the ladder that found the universe accelerating.
Scalar Invariants
Curvature invariants across the Kerr–Newman family — the Abdelqader–Lake, Carminati–McLenaghan and Cartan–Karlhede sets — every closed form pinned against an independent 108-check numerical audit.
Special Relativity
Muons that outlive their lifetime and a jet that fits in a shorter hangar, each told twice, once in each frame: a cosmic-ray shower’s muons falling on their own slowed clocks through an atmosphere contracted in theirs, Frisch and Smith’s Mount Washington count recomputed through the real air, the barn–pole paradox with six real aircraft, the spacetime diagrams boosted from frame to frame, and the crash when the exit never opens.
Doppler & Causality
A source outrunning its own waves, three times: the Mach cone in air, the Cherenkov cone in water with its CODATA thresholds, and the Rindler horizon an accelerating observer builds — where the Minkowski vacuum, cut in two, is exactly a Planck spectrum at the Unruh temperature.
Loop Quantum Gravity
How loops knit space: an arrow carried round a loop on a curved surface comes back turned by the curvature inside, small loops knit into a mesh whose inner edges cancel, a weave of Planck-size rings of spin ½ gives a surface its area one quantum at a time, the area spectrum crowds together into a continuum, and in between lies the mesoscale, where the counted quanta become a noisy field.
The Intrinsic Hamilton–Jacobi Equation
What a diffeomorphism does to a map and to a semi-classical map, and why the evolution is read at a boundary: a map read actively and passively, a chart’s pole, rays folding into a caustic that a point map moves but cannot make, a timeless system read by its clocks, Cartan’s tube, whose open arcs change only at their ends, and Schwarzschild sliced from static to Painlevé, its mass read on a boundary sphere.
Mathematics & Machines
Platonic & Catalan Solids
Every Platonic, Archimedean and Catalan solid constructed, not tabulated: mirrors recovered from Coxeter diagrams, vertex orbits closed by reflection, and the snub cube's tribonacci coordinate proving no compass will draw it.
The Riemann Sphere
The complex plane closed up by its point at infinity: the stereographic projection and the circles and angles it keeps, the four kinds of Möbius map as flows on the sphere, rational functions counted with ∞, a spin’s Majorana stars, and the sky a moving observer sees, where aberration is one Möbius map.
Neural Playground
Three small networks trained live by real backpropagation: a dense net finding π in a circle, a convnet telling discs from rings from sticks, and a recurrent net that can memorise π's digits but never predict them.
Pascal's Triangle
Colour C(n,k) by a rule and watch the patterns fall out: the Sierpinski gasket from parity, its mod-p cousins by Lucas's theorem, Kummer's carries as brightness, the hidden diagonals, a census law for the gasket's dimension — and a sieve on the triangle where every elimination is a theorem.
Cycloids
A point on a rolling wheel: the cycloid and its trochoids; the cardioid, nephroid, deltoid and astroid with their cusps and closures; the evolute that is another cycloid; Roberval's 3πr² slice by slice; the caustic in a coffee cup; and the Spirograph's gcd arithmetic — every length and area computed exactly.
Special Functions
Rodrigues’ formula differentiated rung by rung until the polynomial appears, each derivative gaining a zero; Legendre functions of any degree, the degree a conducting cone chooses, multipoles and spherical harmonics; Airy’s functions at a turning point and under a neutron bouncing on a mirror; Sonine polynomials in a hard-sphere gas; zeros as charges and as Gauss nodes; and the limits that join the families.
Div, Grad, Curl
Vector fields and their three derivatives: the Jacobian at a point split into expansion, rotation and shear, with a parcel and a paddle wheel; landscapes and their paths of steepest descent; line charges, dye blobs and the divergence theorem; wheels in a vortex zoo, Ampère’s wires and a spinning cylinder’s lift; Gauss and Stokes in space; and Helmholtz’s split of any field.
Logic Gates
Boolean gates run gate by gate, each one delay: the seven gates and NAND building them all, the switches and CMOS transistors they are made of, a loop of gates that remembers (the SR latch, a gated latch, a flip-flop), a ripple-carry adder whose sums are wrong until the carry arrives, subtraction as A + ¬B + 1 with its overflow flag, and a clocked accumulator with a fastest safe clock.