physics

PHYSICS LAB

Explore interactive 3D simulations of fundamental physics. From chaotic attractors to quantum probability clouds. Adjust variables in real-time and watch the universe respond.

79 interactive simulations

Lorenz Attractor

3D butterfly orbits through phase space. Adjust σ, ρ, β to trigger chaos onset.

ẋ=σ(y−x), ẏ=x(ρ−z)−y, ż=xy−βz

Double Pendulum

Chaotic motion paints rainbow trails. Run 1–5 pendulums and watch them diverge.

Lagrangian mechanics (RK4)

Reaction-Diffusion

Turing patterns: spots morph into stripes. 6 presets, 6 color themes, paint mode.

∂u/∂t=Dᵤ∇²u−uv²+F(1−u)

Bifurcation Map

Zoom into the Feigenbaum cascade. Watch period-doubling route to chaos.

xₙ₊₁ = r·xₙ·(1−xₙ)

Projectile Motion

Angle, velocity, gravity, air drag. Planet gravity presets: Moon, Mars, Earth, Jupiter.

x=v₀cosθ·t, y=v₀sinθ·t−½gt²

Spring-Mass SHM

Phase space portrait, energy graph, underdamped / critical / overdamped detection.

mẍ + bẋ + kx = 0

N-Body Gravity

Galaxy collision, figure-8, solar system presets. Leapfrog integration.

F=Gm₁m₂/(r²+ε²)

Coupled Oscillators

Normal modes, beat patterns, phase space portrait. In-phase vs out-of-phase presets.

m₁ẍ₁=−k₁x₁+k₂(x₂−x₁)

Orbital Mechanics

Kepler's laws, swept area demo, Hohmann transfer, binary star, solar system.

v²=GM(2/r−1/a)

Lissajous Figures

Rainbow gradient curves. 9 preset thumbnails, 3D isometric mode, projection panels.

x=A·sin(at+δ), y=B·sin(bt)

Collision Simulator

Elastic/inelastic, 1D/2D billiard, momentum & KE bar charts, Web Audio click.

v₁'=[(m₁−em₂)v₁+(1+e)m₂v₂]/(m₁+m₂)
📉

Brachistochrone Curve

Fastest descent curve race: Cycloid vs. Straight line, Circle, and Parabola.

T[y] = ∫ √(1 + y'²) / √(2gy) dx
🔄

Gyroscope Precession

Spinning flywheel precession and nutation with vector overlays and mass badges.

Ωp = m·g·r / (I·ω_s)
🪐

Three-Body Problem

Gravitational chaos and Figure-8 orbit with RK4 integration and mass badges.

F_i = Σ G·m_i·m_j / |r_j - r_i|³ · (r_j - r_i)
🎯

Rutherford Scattering

Alpha particle Coulomb repulsion off gold nucleus, impact parameter b, and scattering angle.

dσ/dΩ = (z Ze² / 16πε₀ E)² / sin⁴(θ / 2)
🕳️

Gravitational Lensing

Schwarzschild Black Hole ray tracer, photon sphere orbit at 1.5 r_s, and deflection angle.

α = 4GM / (c² b) = 2 r_s / b
🪞

Michelson-Morley

Ether drift hypothesis test, perpendicular laser arms, and interference fringe shifts.

ΔN = (2 L / λ) · (v² / c²)
⏱️

Kater's Pendulum

Precision local gravity g measurement via period matching T₁ = T₂ on reversible knife-edge pivots.

g = 4π² L / T²
📈

Quantum Harmonic Oscillator

Hermite-Gaussian eigenstates ψ_n(x), energy level ladder E_n = ℏω(n + 1/2), and coherent states.

E_n = ℏω (n + ½)

Mach-Zehnder

Single-photon quantum optics, phase shift φ, and P1/P2 detector probabilities.

P(D₁) = sin²(φ / 2)
🌀

Poincaré Section

Driven damped pendulum phase space sampling once per period revealing fractal strange attractors.

d²θ/dt² + b·dθ/dt + sin θ = F₀cos(ω_dt)

Hall Effect

Semiconductor charge carrier drift under B-field creating Hall voltage VH = IB/nqt.

V_H = (I · B) / (n · q · t)
📻

Cavity Resonator

Rectangular metallic cavity TE_mn & TM_mn electromagnetic standing modes.

f_mn = (c / 2) · √[(m / a)² + (n / b)²]
🔊

Acoustic Levitation

Ultrasonic 40 kHz standing wave Gor'kov radiation force trapping beads at pressure nodes.

F_rad = -∇ U_gorkov
🌊

Davisson-Germer

de Broglie electron matter wave diffraction off nickel crystal lattice & 54V scattering peak.

λ = h / p = 1.226 / √V
🧲

Meissner Effect

Superconducting magnetic flux expulsion B = 0 below Tc and quantum flux pinning levitation.

B(x) = B₀ · e^(-x / λ_L)

Stern-Gerlach

Quantum electron spin quantization Sz = ±ℏ/2 beam splitting in inhomogeneous B-field.

F_z = ± (g_s μ_B / 2) · (∂B_z / ∂z)
⚖️

Mass Spectrometer

Isotope separation by m/q ratio via velocity selector E/B1 and deflection radius r = mv/qB2.

r = (m · v) / (q · B)
🪞

Fabry-Pérot

Optical cavity resonator, finesse F = π√R/(1-R), and sharp Airy transmission peaks.

T = 1 / [1 + F · sin²(δ / 2)]
🔵

Cherenkov Radiation

Relativistic v > c/n particle emitting blue optical shockwave cone cos θ = 1/(βn) in water.

cos θ_C = 1 / (β · n)

Dirac Monopole

Isolated magnetic charge qm, vector potential Dirac string tube, and charge quantization qe qm = 2πℏn.

q_e · q_m = 2π ℏ n
🎯

Mössbauer Effect

Recoil-free Fe-57 gamma resonance in solid lattice and Doppler velocity vD hyperfine scanning.

f = exp[ - (k² ⟨x²⟩) ]
📈

Quantum Hall Effect

Quantized Hall resistance Rxy = h/(νe²) = RK/ν and topological skipping orbit edge states.

R_xy = h / (ν e²) = R_K / ν
📐

Brillouin Zones

Reciprocal k-space lattice vectors, Bragg reflection bisector planes, and Wigner-Seitz cell.

k · (G / 2) = (G / 2)²

Aharonov-Bohm

Quantum vector potential phase shift Δφ = eΦ/ℏ around shielded magnetic solenoid B = 0.

Δφ = (e / ℏ) ∮ A · dr
☀️

Magnetic Reconnection

Solar flare energy release, X-line B-field snapping, and Alfvénic outflow jets vA = B/√(μ₀ρ).

v_A = B / √(μ₀ · ρ)

Superfluid Fountain

Liquid Helium-4 two-fluid model below Tλ = 2.17 K & thermomechanical fountain pressure ΔP = ρSΔT.

ΔP = ρ · S · ΔT
🕳️

Kerr Ergosphere

Rotating black hole Penrose process energy extraction Eout > Ein from frame-dragging ergosphere.

r_E = M + √(M² - a² cos²θ)
🔴

Quantum Dot

3D quantum confinement Brus bandgap shift Eg(R) and size-dependent QLED photoluminescence color.

E_g(R) = E_bulk + (ℏ²π²) / (2m*R²)

Josephson Junction

Cooper pair tunneling I = Ic sin φ, AC oscillations fJ = 2eV/h, and SQUID magnetometry.

I = I_c · sin(φ)
🧲

Casimir Effect

Quantum vacuum zero-point energy attraction F/A = ℏcπ²/(240d⁴) between gold plates.

F / A = (ℏ c π²) / (240 d⁴)
📊

HBT Effect

Photon statistics & second-order coherence g²(τ), thermal bunching vs quantum antibunching.

g²(τ) = ⟨I(t)I(t+τ)⟩ / ⟨I(t)⟩²
🌀

Kelvin-Helmholtz

Fluid shear velocity differences U1 vs U2 generating spiral vortex billows for Ri < 0.25.

Ri = -(g / ρ) · (∂ρ/∂z) / (∂u/∂z)²
🍄

Rayleigh-Taylor

Heavy fluid above light fluid under gravity creating Atwood A mushroom finger plumes.

A = (ρ₁ - ρ₂) / (ρ₁ + ρ₂)
🔊

Chladni Patterns

Acoustic resonance figures. Sand particles drift to nodal lines with audio synthesis.

w(x,y) = cos(nπx)cos(mπy) - cos(mπx)cos(nπy)

Fourier Series

Rotating epicycles build square, triangle, sawtooth — or draw your own waveform.

f(t) = Σ Aₙsin(nωt + φₙ)

Ripple Tank

Up to 6 draggable sources, 3 color modes. Shows constructive/destructive bands.

h=Σ Aᵢ·sin(2πfᵢt−kr+φᵢ)·e^(−r/d)

Double Slit Diffraction

N-slit generalization, wavelength color tinting, Huygens wavefront animation.

I(θ)=I₀cos²(πd·sinθ/λ)·sinc²(πa·sinθ/λ)

Standing Waves

Color-breathing nodes/antinodes, traveling wave decomposition, 2D membrane modes.

y(x,t)=2A·sin(kx)·cos(ωt)
))))

Doppler Effect

Mach cone, sonic boom, compressed/stretched wavefronts. Web Audio pitch-shift.

f'=f₀·(v+vo)/(v−vs)

Electric Field Lines

Drag charges around canvas. Field lines, equipotentials, and heatmap redraw instantly.

E=kq/r²

Magnetic Field

Biot-Savart: wire, solenoid, Helmholtz coil. Vector arrows, field lines, heatmap.

B=μ₀I/(2πr)

EM Wave

3D isometric E & B fields, circular polarization, EM spectrum bar.

E(x,t)=E₀·sin(kx−ωt) ŷ

Cyclotron Motion

Pure B field, E×B drift, cyclotron accelerator, magnetic bottle — 4 scenarios.

r=mv/(|q|B), ωc=|q|B/m

RC/LC Circuit

Animated schematic, RC/RL/LC/RLC modes, resonance curve, phasor diagram.

q(t)=Q₀·e^(−Rt/2L)·cos(ωdt)
·:·

Ideal Gas

200–500 bouncing particles, draggable piston, live pressure gauge, PV=nRT graphs.

PV=nRT, KE=½mv²

Maxwell-Boltzmann

Multi-gas, multi-temperature overlay. Animated distribution with v_p, ⟨v⟩, v_rms.

f(v)=4π(m/2πkT)^(3/2)·v²·e^(−mv²/2kT)

Heat Diffusion

Paint hot/cold on canvas while it runs. 4 color themes, 3 boundary conditions.

∂T/∂t = α·∇²T

Particle in a Box

Superposition of 4 states, animated time evolution, 2D box mode.

ψₙ=√(2/L)sin(nπx/L), Eₙ=n²E₁

Quantum Tunneling

Wave packet through barrier, T% vs E curve, double-barrier resonance.

T≈e^(−2κd), κ=√(2m(V₀−E))/ℏ
γ

Photoelectric Effect

5 metals, KE vs frequency graph reveals Planck's constant. Electron ejection animation.

KE=hf−φ, f₀=φ/h

Snell's Law

TIR flash, prism dispersion, beam mode. Drag the ray or use the slider.

n₁·sinθ₁ = n₂·sinθ₂

Thin Lens

3 principal rays, draggable object, real/virtual image detection, mirror mode.

1/f=1/do+1/di, m=−di/do

Time Dilation

Twin clocks, ruler contraction, Minkowski diagram. γ gauge with real-world examples.

γ=1/√(1−β²), Δt'=γ·Δτ

Spacetime Diagram

Minkowski diagram, Lorentz transformation, twin paradox, click to place events.

Δs²=c²Δt²−Δx²

Gravitational Waves

Binary inspiral, test mass ring distortion, LIGO schematic, chirp signal plot.

h=A·cos(2πf_GW·t)

Hydrogen Orbitals

2D cross-section heatmaps for all orbitals up to n=4. Energy level diagram, 3 color schemes.

ψ_nlm=R_nl(r)·Y_lm(θ,φ)
Δ

Uncertainty Principle

Gaussian wave packet, dual x-space / k-space panels, slit diffraction analogy.

Δx·Δp ≥ ℏ/2

Bohr Model

Animated electron transitions, emission spectrum lines, 5 elements, spectral series.

Eₙ=−13.6/n² eV

Nuclear Decay

Probabilistic atom grid, 8 real isotopes, C-14 dating mode, decay chain visualization.

N(t)=N₀·e^(−λt)

Compton Scattering

Photon-electron relativistic scattering, wavelength shift, and recoil momentum.

λ' - λ = λ_C · (1 - cos θ)

Blackbody Radiation

Planck curve colored by actual wavelength, UV catastrophe, star types M→O.

B(λ,T)=(2hc²/λ⁵)/(e^(hc/λkT)−1)

Pendulum Wave

15 rainbow pendulums, glowing trails, wave/diagonal/sync patterns over one cycle.

τ_k=T/(n+k−1), L_k=gτ_k²/4π²
~

Fluid Dynamics

Stable Fluids (Navier-Stokes). Smoke/fire/ocean modes. Mouse-stir the fluid.

∂v/∂t+(v·∇)v=−∇P/ρ+ν∇²v

Bernoulli Effect

Venturi pipe, airfoil lift, Torricelli jet, spinning ball Magnus effect.

P+½ρv²+ρgh=const

EM Induction

Faraday's law: magnet/coil, generator, changing B, moving rod. Live EMF & flux graphs.

EMF=−dΦ/dt

Polarization

Malus's law, 4-polarizer cascade, wave plates, animated E-field oscillation.

I=I₀·cos²θ

Game of Life

Age-colored cells, 20+ patterns, Gosper glider gun, 6 CA rulesets, custom B/S.

B3/S23 — Conway's rules

Fractals

Chaos game (Barnsley fern), Mandelbrot zoom, Julia morph, Newton fractal.

z_{n+1}=z_n²+c
Developer Reference

Core Algorithm & Standalone Script

Standalone, zero-dependency JavaScript implementation powering this tool. Free to inspect, copy, and build upon.

// Filter functionality
    const filterBtns = document.querySelectorAll('.filter-btn');
    const simCards = document.querySelectorAll('.sim-card');

    filterBtns.forEach(btn => {
      btn.addEventListener('click', () => {
        // Remove active state from all buttons
        filterBtns.forEach(b => b.classList.remove('active'));
        // Add active state to clicked button
        btn.classList.add('active');

        const filter = btn.getAttribute('data-filter');

        simCards.forEach(card => {
          const category = card.getAttribute('data-category');
          if (filter === 'all' || category === filter) {
            card.classList.remove('hidden');
          } else {
            card.classList.add('hidden');
          }
        });
      });
    });

    // Update simulation count based on active cards
    function updateCount() {
      const visibleCards = document.querySelectorAll('.sim-card:not(.hidden)').length;
      document.getElementById('sim-total').textContent = visibleCards;
    }

    // Initialize count
    updateCount();

    // Recount when filter changes
    filterBtns.forEach(btn => {
      btn.addEventListener('click', updateCount);
    });