可以拨弄的场与力——涟漪与干涉、轨道与混沌——每一个都实时求解，让规律在你的把玩中自行显现。
A Gaussian packet built from a band of wavenumbers moves at its group velocity while the carrier slips through at the phase velocity.
A finite-difference string solves the 1D wave equation, reflecting and resonating as you drive or pluck it.
A bluff body sheds alternating vortices into a Kármán street, traced by drifting dye streaklines.
A self-sustaining nonlinear oscillator whose limit cycle attracts every start and sharpens into relaxation pulses.
A pulse races down a line and reflects off the load — open, short, matched, or anything between.
A moving light clock ticks slower by the Lorentz factor γ, and the twins age apart.
A self-bound moon swings past a planet and stretches — disrupting into a stream past the Roche limit.
Trace the three principal rays through a converging or diverging lens to build the image it forms.
The swirling colours of soap bubbles and oil slicks, computed from the interference of light reflected off a film just a few hundred nanometres thick.
A torque-free body spun about its middle principal axis flips end over end — the Dzhanibekov effect.
Two travelling waves run in opposite directions and lock into a standing pattern of nodes and antinodes.
The Chirikov standard map: smooth KAM tori shattering into a chaotic sea as the kick strength rises.
A line of beads on springs carries transverse waves that reflect off fixed ends into standing patterns.
A heavy symmetric top precessing on a fixed point, its tip tracing the classic looping nutation curves.
Reflect the principal rays off a concave or convex mirror to construct the image it returns.
Smoothed-particle hydrodynamics: a thousand particles slosh and splash with pressure, viscosity, and gravity.
A ray crosses the boundary between two media — watch it bend, split, and trap itself past the critical angle.
Buoyant smoke billows through a Stable-Fluids solver with thermal lift and vorticity confinement.
A single aperture spreads light into a broad central maximum flanked by weaker side lobes — the Fraunhofer sinc² pattern.
Topological kinks, kink–antikink collisions, and an oscillating breather in the relativistic nonlinear wave equation u_tt − u_xx + sin u = 0.
A source outrunning its own sound stacks wavefronts into a Mach cone — the geometry of the sonic boom.
The 2D shallow-water equations spread ripples and break dams across a shaded-relief pool.
P and S waves race from a quake epicenter, refracting through Earth layers, and the S−P gap times the distance.
A wave packet flies across a plane and scatters off slits, wells, and barriers in glowing interference.
A single spiralling fold in 3D: the minimal Rössler flow tracing its banded strange attractor.
A pen riding a circle that rolls along a line or another circle traces cycloids, epicycloids, and hypocycloids.
A series RLC loop rings, decays, and resonates as you tune R, L, C and the source.
Light from a moving source blueshifts ahead and redshifts behind, with a transverse shift at 90°.
At near-light speed the stars crowd ahead and shift color — the relativistic headlight effect.
A Gaussian wave packet strikes a barrier — watch it split, with part reflecting and part tunneling clean through.
A shot fired through air, its quadratic-drag arc skewed against the ideal vacuum parabola.
White light enters a glass prism and fans out into a spectrum because the index of refraction depends on colour.
A small 1/r³ correction turns Newton’s closed ellipse into a slowly rotating rosette.
Send light through a polarizer, a wave plate and an analyzer; trace the E-field's spinning ellipse and read the transmitted intensity off Malus's law.
Fill a grid cell-by-cell and watch a spanning cluster snap into existence at the critical threshold.
A rack of pendulums with finely graded lengths drifts through travelling waves, chaos, and a clean realignment.
Stack the sine-wave eigenstates of an infinite well and watch their superposition breathe and slosh.
A Hohmann transfer: two prograde burns lift a craft between coplanar circular orbits.
Two worlds locked near a small-integer period ratio, pumping each other through repeated conjunctions.
A sandbox: drop lenses and apertures on a rail and watch a fan of rays bend through them in sequence.
A plano-convex lens on a flat plate traps a wedge of air whose thickness paints concentric interference rings — dark at the centre, radii growing as √m.
A row of swinging balls passes momentum cleanly down the line through near-elastic collisions.
A cold cloud of stars collapses, scatters, and virializes under its own gravity.
Split a beam, reflect it off two mirrors, recombine — and watch concentric fringes born and swallowed as one mirror creeps by half a wavelength.
The standing eigenmodes of a vibrating drumhead, rendered as a living heatmap of nodal lines.
Electromagnetic waves radiate, reflect, and diffract through a slit in a live 2D solution of Maxwell's equations.
A tiny gatekeeper sorts fast molecules from slow ones, conjuring a temperature gap from a uniform gas — the thought experiment that haunts entropy.
Start every disk at the same speed and watch elastic collisions sculpt the gas into the Maxwell–Boltzmann distribution.
A spinning cylinder bends the flow and a spinning ball curves through the air under the Magnus force.
An iron bob swinging over a ring of magnets, settling onto fractal basins of attraction.
Currents perpendicular to the plane curl the magnetic field around them; build single wires, pairs, or a solenoid cross-section.
The butterfly-shaped strange attractor of atmospheric convection, traced in 3D.
An interactive Minkowski diagram where a boost scissors the axes toward the light cone.
The period-doubling road to chaos in xₙ₊₁ = r·xₙ(1−xₙ), as a bifurcation diagram linked to a live cobweb.
The causal structure of spacetime in 2+1D — past, future, and the unreachable elsewhere.
A 2D molecular dynamics box where a single pair potential drives matter between gas, liquid and a hexagonal solid.
A D2Q9 lattice-Boltzmann fluid streams past an obstacle and sheds a Kármán vortex street.
The five equilibria of the restricted three-body problem, drawn on the rotating effective potential.
A swarm of coupled phase oscillators that spontaneously synchronize once coupling crosses a critical threshold.
A single body sweeping a conic orbit, painting equal areas in equal times.
Tall waves overtake short ones and pass clean through, re-emerging unchanged — the Korteweg–de Vries equation that first revealed the soliton.
Shake a pendulum’s pivot fast enough and the upside-down position turns from unstable to rock steady.
Metropolis Monte Carlo on a lattice of spins — cross the critical temperature Tc ≈ 2.269 and watch a ferromagnet spontaneously order.
A box of hard disks bouncing off a movable piston — measure pressure from wall impacts and watch PV = NkT emerge.
Sample the electron probability cloud |ψₙₗₘ|² of hydrogen as a 3D point cloud you can orbit.
Every point of a wavefront is a source of secondary wavelets whose envelope rebuilds — and bends — the advancing front.
Paint hot and cold onto a metal plate and watch temperature diffuse by the explicit FTCS solution of ∂T/∂t = α∇²T.
Hermite–Gaussian eigenstates on a parabolic well, and coherent states that slosh like a classical particle.
A fast-spinning rotor on a pivot whose angular momentum makes it precess and nutate instead of falling.
Two diffusing chemicals react and feed back, growing spots, stripes, mazes and self-dividing cells from the famous Pearson map.
A spacecraft slingshots past a moving planet, stealing speed from its orbital motion.
A point mass bends background light into multiple images and a glowing Einstein ring.
Thousands of grains collide through spring-dashpot contacts, heaping into a pile or draining an hourglass.
A train of meshing spur gears whose tooth-count ratios set the speed and direction of every shaft.
Balls bounce through a triangle of pegs and pile up into a binomial that converges on the bell curve.
Two disk galaxies pass and tear each other into tidal tails and bridges.
Energy loaded into one mode of a nonlinear spring lattice refuses to thermalise and almost perfectly returns — the Fermi–Pasta–Ulam–Tsingou recurrence.
Stack sine harmonics into square, saw and triangle waves and watch the partial sum converge with Gibbs ringing.
A long pendulum whose swing plane slowly rotates as the Coriolis force betrays Earth's spin beneath it.
Launch a ray into a step-index fiber and watch total internal reflection guide it — or leak it away outside the acceptance cone.
Sweep a bar magnet through a coil; the changing flux induces an EMF and Lenz-law current, traced live on a scope.
A travelling electromagnetic plane wave with mutually perpendicular E and B fields and E×B propagation.
Drag point charges on the plane and watch field lines and equipotentials reshape by Coulomb superposition.
A forced double-well oscillator whose Poincaré section strobes out a fractal strange attractor.
A damped mass on a spring pushed by a periodic force, climbing toward resonance as the drive nears its natural frequency.
Two coherent sources overlap into Young's bright-and-dark fringes, with the live interference field above its intensity pattern.
Two coupled arms whose exact equations of motion descend into deterministic chaos.
A moving source bunches its wavefronts ahead and stretches them behind, forming a Mach cone past the speed of sound.
An oscillating electric dipole sheds propagating field ripples and the textbook sin²θ radiation donut.
Random walkers wander until they touch a growing cluster and freeze, sculpting a fractal dendrite.
N coherent slits sharpen the interference pattern into needle-thin spectral orders set by d·sinθ = mλ.
A charged particle spirals outward as resonant kicks across the dee gap pump it to higher energy.
A supercooled melt nucleates seeds that grow into oriented crystal grains, meeting at sharp boundaries.
Two pendulums linked by a spring trade energy back and forth in slow beats built from two normal modes.
A Verlet-integrated mesh of point masses and distance constraints ripples and drapes under wind and gravity.
The simplest chaotic electronic circuit, whose piecewise-linear diode folds current into a 3D double-scroll attractor.
Drive a square plate at an eigenmode and sand drifts to the nodal lines, tracing the classic Chladni figures.
A charge in uniform E and B fields spirals, drifts, and helixes — integrated with the energy-conserving Boris pusher.
A hanging chain of constrained beads settling into the cosh curve, with an analytic fit overlaid.
Drive an ideal-gas piston through the four reversible strokes of the perfect heat engine and trace its closed loop on the P–V plane.
A parallel-plate capacitor with edge fringing and a sliding dielectric slab; watch C, V, E and stored energy respond.
A heavy pollen grain jitters under the relentless drumming of invisible molecules — its random walk grows as ⟨r²⟩ ∝ t.
Three beads race between the same two points and the cycloid — not the straight line — always wins.
Steer a single qubit on the Bloch sphere with quantum gates and continuous rotations.
An excitable FitzHugh–Nagumo medium where broken wavefronts curl into the counter-rotating spirals and target rings of the BZ reaction.
Sum two close tones and a slow beat envelope rises and falls at exactly their frequency difference.
The Kronig–Penney model: a periodic lattice splits free-electron energies into allowed bands and forbidden gaps.
A line of isotropic emitters whose progressive phase steers the radiated beam with no moving parts.
Potential flow around a Joukowski airfoil with Kutta-set circulation, drawn as streamlines and a pressure map.
Coherent speakers paint a standing lattice of loud antinodes and silent nodal lines you can reshape by dragging.
Rotating phasors and the impedance triangle of a series R-L-C circuit reveal phase lead and lag.
完全在 GPU 上求解的实时二维纳维-斯托克斯方程——用光标涂抹涡量，看墨水以 60 fps 旋卷并耗散。
由 WebAssembly 驱动的二维波动实验室——实时开展干涉、衍射、折射与反射实验。
实时测地线追踪的双黑洞并合——当两个事件视界相互螺旋靠近、啁啾并衰荡时，光线在其周围弯曲。仅支持 WebGPU。
引力三体运动的混沌，实时积分求解。