Physics Lab

∞

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)

∿

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)

★

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