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Galton Board - A Demonstration of Central Limit Theorem

Parameters
Live Data
Total Balls Landed
0
Empirical Mean (μ)
0.00
Std Deviation (σ)
0.00
Bars auto-scale to fit data.
Magenta Curve = Normal Distribution

Beautiful Monte Carlo Density Cloud and Solid Surface Visualizations of Atomic Orbitals

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RESOLVING WAVEFUNCTION...
Quantum Mechanics

Interactive Atomic Orbital Visualization

Explore immersive 3D atomic orbital visualizations generated from quantum mechanical wavefunctions. Interactively study electron probability clouds, nodal surfaces, spherical harmonics, and orbital symmetries for s, p, d, f and g orbitals.

What Are Atomic Orbitals?

Atomic orbitals are quantum wavefunctions that describe the probable location of electrons around atomic nuclei.

Visualization Features

  • 3D Orbital Rendering
  • Electron Cloud Simulation
  • Cross Section Slicing
  • Physics Basis Mode
  • Real-Time GPU Rendering

Supported Orbitals

Visualize: 1s, 2p, 3d, 4f, 5g and many other quantum states.

Educational Applications

Ideal for physics students, chemistry education, quantum mechanics lectures, STEM demonstrations, and atomic structure exploration.

Orbital Explorer

1s

Solid Isosurface

The Onset of Chaos - Double Pendulum

Equations of Motion
$$\begin{aligned} \ddot{\theta}_1 &= \frac{-g(2M_1+M_2)\sin\theta_1 - M_2 g \sin(\theta_1-2\theta_2) - 2\sin(\theta_1-\theta_2)M_2(\dot{\theta}_2^2 L_2 + \dot{\theta}_1^2 L_1 \cos(\theta_1-\theta_2))}{L_1(2M_1+M_2-M_2\cos(2\theta_1-2\theta_2))} \\[10pt] \ddot{\theta}_2 &= \frac{2\sin(\theta_1-\theta_2)(\dot{\theta}_1^2 L_1(M_1+M_2) + g(M_1+M_2)\cos\theta_1 + \dot{\theta}_2^2 L_2 M_2 \cos(\theta_1-\theta_2))}{L_2(2M_1+M_2-M_2\cos(2\theta_1-2\theta_2))} \end{aligned}$$

Onset of Chaos

Base Angle $\theta_1$
Base Angle $\theta_2$
Separation $\Delta\theta$