Humanitarians AI
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Simulations

108 interactive simulations.

Wave Packet Spreading — Group vs Phase Velocity

Uncertainty Minimizer — σₓ · σₚ ≥ ħ/2

Infinite Well Superposition — Quantum Sloshing

Coherent State Oscillator

Spin-½ Uncertainty Ensemble

Spherical Harmonics & Angular Momentum Cone

Sequential Stern-Gerlach — Born Rule & Measurement Disturbance

Hydrogen Radial Probability Density

08 — Two-Particle Symmetry: Bosons, Fermions, Distinguishable

Asymptotic Series & Perturbation Theory — Anharmonic Oscillator

Hydrogen Stark Effect — n=2 Shell

Rabi Oscillations vs Perturbation Theory

Geiger-Nuttall Law — Alpha Decay & Gamow Tunneling

Tunneling Wave Packet — Crank-Nicolson TDSE

WKB vs Exact Transmission — Rectangular Barrier

CHSH Bell Inequality

Bloch Sphere Decoherence — T₁, T₂, T_φ

NV Center ODMR — Quantum Magnetometry

BGP vs Bellman-Ford: Counting to Infinity

Bloch Sphere Qubit Explorer

Borwein Integrals: A Pattern That Breaks at Step 8

Covering Rationals: A Dense Set With Measure Zero

Curse of Dimensionality: Local Becomes Global

CV Filter Leakage: 5000 Random Predictors Report 0% Error

Epidemic Growth Factor: One Month's Warning

FFT vs Naive Convolution: A 1000× Speedup from Math

The Fourier Transform: Winding a Signal Around a Circle

Fractal Dimension: Between Curve and Plane

Gene Drive: One Edit Floods a Million Mosquitoes

Hairy Ball Theorem — Vector Fields on S²

Hermitian Eigenvalue Explorer

High-D Sphere Volume: Peaks at n=5, Then Shrinks to Zero

The Inner Sphere Paradox: It Pokes Outside the Box in 10D

Karatsuba Multiplication: 3 Recursive Calls Beat 4

Knapsack's Hidden Exponential: One Zero, Ten Times Slower

Kolmogorov Turbulence: The −5/3 Power Law Hidden in Chaos

LASSO vs Ridge: Why a Diamond Beats a Circle for Sparsity

Exchange Symmetry & Pauli Exclusion Node

Hydrogen Radial Explorer — Sweep n, ℓ

Hydrogen Atom — Energy Levels & Transitions

Madelung Exceptions — 3d Transition Metals

Rabi Oscillation — Spin Flopping Between Up and Down

Robertson Bound on the Bloch Sphere

CHSH Bell Inequality Tester

Fermi's Golden Rule — Transition Probability

Finite Square Well Explorer — 1D vs 3D

Harmonic Oscillator Ladder — Uncertainty Floor

Kronig-Penney Band Gap Explorer

Quantum Statistics Explorer

Uncertainty Principle Explorer

Variational Helium — Screened Nuclear Charge

Quantum Revival Explorer — Superposition Breathing in a Box

SIR Epidemic: How One Hub Defeats Social Distancing

Sturm-Liouville Orthogonality Gallery

Uncertainty Principle Sandbox

Variational Bound Optimizer

Barrier Transmission Explorer — Exact vs WKB

Bloch Sphere — Qubit State & Robertson Uncertainty Bound

de Broglie Wavelength Scale

Finite Square Well Explorer

Planck vs Rayleigh-Jeans — UV Catastrophe

Uncertainty Hyperbola — σₓ × σₚ ≥ ℏ/2

Born Approximation Validity Map

Hard-Sphere Quantum Scattering Cross Section

Kronig-Penney Band Structure Explorer

Quantum Dot Confinement — CdSe Brus Equation

Rabi Detuning Landscape — Resonance and Off-Resonance

Sinc² → Fermi's Golden Rule

Zeeman Crossover — Hydrogen 2p Manifold

CHSH Angle Explorer — Why 45° Wins

Entanglement Entropy — The Ebit Curve

NV Center ODMR — Magnetic Field Map

Partial Trace — Tracing Away One Qubit Kills All Coherence

Quantum Platform N_gates Comparison

Willow Threshold Reconstruction — Surface Code Error Rates

Wallis Product: Two Diverging Halves Converge to π/2

Multi-Armed Bandit: Explore vs Exploit

Braess's Paradox

CLT: Repeated Convolution

Hanoi ↔ Binary Counting

Mandelbrot & Julia Sets

Moser's Circle

Newton's Fractal

Phase Transition — Free Energy

Pi from Block Collisions

Prime Polar Spirals

Putnam: Simplex Contains Center

Rocket Equation Tyranny

Square-Cube Metabolic Law

Three Polarizer Paradox

Windmill Invariant — IMO 2011

Argentine Ant Supercolony: Genetic Diversity as a Phase Transition

Bagging: 300 Trees Kill the Variance

The Basel Problem: Lighthouses Sum to π²/6

Why Doctors Get Medical Tests Wrong: Bayes Factor

Bias-Variance Tradeoff: The U-Shaped Test Error

Binomial → Normal: The Central Limit Theorem in Action

Bloom Filter: Exponential Precision for Linear Space

Braess's Paradox: The Road That Slows Everyone

Cache Replacement: FIF vs LRU vs FIFO

The Central Limit Theorem: Any Shape Becomes a Bell

Complex Systems: One Local Rule, No Central Plan

Binary Counting Solves Towers of Hanoi

Greedy Knapsack: The 50% Guarantee

Mandelbrot Set Hidden Inside Newton's Method

Block Collisions Count π: The Configuration Space View

Quicksort Harmonic Analysis

Six Dots Make 31, Not 32: When Patterns Break

Humanitarians AI Lyrical Literacy Project